Inclusion Criteria:

          -  Non-small cell lung cancer (NSCLC) with an activating EGFR mutation (exon 19 deletion,
             L858R point mutation, or any other mutation known to be associated with EGFR TKI
             sensitivity); presence of an activating EGFR mutation may be documented in tumor
             tissue or by plasma testing if performed in a Clinical Laboratory Improvement Act
             (CLIA)-certified laboratory

          -  No prior treatment with an EGFR TKI; patient may have received prior chemotherapy for
             early-stage or advanced disease but this is not required; prior immunotherapy is not
             allowed

          -  Patients must have at least one measurable CNS lesion that is asymptomatic, untreated,
             and does not require local therapy at the time of enrollment; measurable CNS disease
             is defined as a brain metastasis that can be accurately measured in at least one
             dimension (longest diameter to be recorded) as >= 5 mm (>= 0.5 cm) with brain magnetic
             resonance imaging (MRI); if the lesion is 5-10 mm in size and is the only measurable
             disease, MRI imaging must be performed with 1.5 mm slice thickness or less; a history
             of previously treated brain metastases is allowed, however any lesion present at the
             time of whole brain radiotherapy or included in the stereotactic radiotherapy field
             (or within 2 mm of the treated lesion) will NOT be considered "untreated" unless it is
             new or documented to have progressed unequivocally since treatment

          -  Patients are not required to have measurable systemic (i.e. non-CNS) disease; if
             present, measurable systemic disease must be able to be accurately measured in at
             least one dimension (longest diameter to be recorded for non-nodal lesions and short
             axis for nodal lesions) as >= 20 mm (>= 2 cm) with conventional techniques or as >= 10
             mm (>= 1 cm) with spiral computed tomography (CT) scan, MRI, or calipers by clinical
             exam

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2

          -  Life expectancy of greater than 3 months

          -  The use of anti-convulsants is allowed, as long as the patient is on a stable dose
             with no seizure activity for at least 2 weeks prior to initiating trial therapy

          -  Female subjects should be using highly effective contraceptive measures, and must have
             a negative pregnancy test and not be breast-feeding prior to start of dosing if of
             child- bearing potential or must have evidence of non-child-bearing potential by
             fulfilling one of the following criteria at screening:

               -  Post-menopausal defined as aged more than 50 years and amenorrheic for at least
                  12 months following cessation of all exogenous hormonal treatments

               -  Women under 50 years old would be consider postmenopausal if they have been
                  amenorrheic for 12 months or more following cessation of exogenous hormonal
                  treatments and with luteinizing hormone (LH) and follicle stimulating hormone
                  (FSH) levels in the post-menopausal range for the institution

               -  Documentation of irreversible surgical sterilization by hysterectomy, bilateral
                  oophorectomy or bilateral salpingectomy but not tubal ligation

          -  Fertile men should be willing to use barrier contraception during and for 4 months
             after AZD9291 (osimertinib), and fertile women must agree to use adequate
             contraceptive measures during and for 6 weeks after AZD9291 (osimertinib); fertile men
             and women must agree to use adequate contraceptive measures during study therapy and
             for at least 6 months after the completion of bevacizumab therapy; should a woman
             become pregnant or suspect she is pregnant while she or her partner is participating
             in this study, the patient should inform the treating physician immediately

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Symptomatic brain metastases or symptomatic leptomeningeal disease; asymptomatic
             leptomeningeal disease is allowed

          -  Patients with brain metastases for whom complete surgical resection is clinically
             appropriate

          -  Prior treatment with any EGFR TKI

          -  Prior treatment with agents targeting the VEGF pathway, including bevacizumab

          -  The use of corticosteroids to control cerebral edema or treat neurologic symptoms will
             not be allowed, and patients who previously required corticosteroids for symptom
             control must be off steroids for at least 3 days without recurrence of symptoms prior
             to starting trial therapy; corticosteroids for other indications is allowed

          -  Patients may not be receiving any other investigational agents and may not have
             participated in a study of an investigational agent or using an investigational device
             within five half-lives of the compound or 3 months, whichever is greater

          -  Any unresolved toxicities from prior therapy greater than Common Terminology Criteria
             for Adverse Events (CTCAE) grade 1 at the time of starting study treatment with the
             exception of alopecia and grade 2 platinum-therapy related neuropathy

          -  Concurrent, active malignancies in addition to that being studied (other than
             cutaneous squamous cell carcinoma or basal cell carcinoma)

          -  Any contraindication to MRI (i.e. patients with pacemakers or other metal implanted
             medical devices)

          -  Past medical history of interstitial lung disease, drug-induced interstitial lung
             disease, radiation pneumonitis which required steroid treatment, or any evidence of
             clinically active interstitial lung disease

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to AZD9291 (osimertinib) or bevacizumab

          -  Urine protein should be screened by urine analysis; if protein is 2+ or higher,
             24-hour urine protein should be obtained; patients with 24-hour urine protein >= 1000
             mg are excluded

          -  Serious or non-healing wound, ulcer or bone fracture

          -  History of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess
             within 6 months prior to day 1

          -  Invasive procedures defined as follows:

               -  Major surgical procedure, open biopsy or significant traumatic injury within 28
                  days prior to day 1 therapy

               -  Anticipation of need for major surgical procedures during the course of the study

               -  Core biopsy within 7 days prior to day 1 (D1) therapy

          -  Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or
             recent peripheral arterial thrombosis) within 6 months prior to day 1

          -  Patients with clinically significant cardiovascular disease are excluded

               -  Inadequately controlled hypertension (HTN) (systolic blood pressure [SBP] > 160
                  mmHg and/or diastolic blood pressure [DBP] > 90 mmHg despite antihypertensive
                  medication)

               -  History of cerebrovascular accident (CVA) within 6 months (see additional
                  requirement for adjuvant protocols)

               -  Myocardial infarction or unstable angina within 6 months (see additional
                  requirement for adjuvant protocols)

               -  New York Heart Association grade II or greater congestive heart failure

               -  Serious and inadequately controlled cardiac arrhythmia

               -  Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection)

               -  Clinically significant peripheral vascular disease

          -  Any of the following cardiac criteria:

               -  Mean resting corrected QT interval (Fridericia's correction formula [QTcF]) > 470
                  ms obtained from 3 electrocardiograms (ECGs), using the screening clinic ECG
                  machine derived corrected QT (QTc) value

               -  Any clinically important abnormalities in rhythm, conduction or morphology of
                  resting ECG (e.g., complete left bundle branch block, third degree heart block,
                  second degree heart block)

               -  Any factors that increase the risk of QTc prolongation or risk of arrhythmic
                  events such as heart failure, hypokalemia, congenital long QT syndrome, family
                  history of long QT syndrome or unexplained sudden death under 40 years of age in
                  first degree relatives or any concomitant medication known to prolong the QT
                  interval

          -  Evidence of bleeding diathesis or coagulopathy (including clinically significant
             hemoptysis)

          -  Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to
             swallow the formulated product or previous significant bowel resection that would
             preclude adequate absorption of AZD9291 (osimertinib)

          -  Patients with known hypersensitivity to Chinese hamster ovary cell products or other
             recombinant human antibodies

          -  Patients currently receiving (or unable to stop use prior to receiving the first dose
             of study treatment) medications or herbal supplements known to be potent inducers of
             CYP3A4 (at least 3 weeks prior); all patients must try to avoid concomitant use of any
             medications, herbal supplements and/or ingestion of foods with known inducer effects
             on CYP3A4

          -  Any evidence of severe or uncontrolled systemic diseases, including, but not limited
             to, uncontrolled hypertension, symptomatic congestive heart failure, unstable angina
             pectoris, cardiac arrhythmia, or psychiatric illness/social situations which in the
             investigator's opinion makes it undesirable for the patient to participate in the
             trial or which would jeopardize compliance with the protocol, or active infection
             including hepatitis B, hepatitis C and human immunodeficiency virus (HIV); screening
             for chronic conditions is not required

          -  History of hypersensitivity active or inactive excipients of AZD9291 (osimertinib) or
             drugs with a similar chemical structure or class to AZD9291 (osimertinib)

          -  Absolute neutrophil count < 1.5 x 10^9/L

          -  Platelet count < 100 x 10^9/L

          -  Hemoglobin < 90 g/L

          -  Alanine aminotransferase > 2.5 times upper limit of normal (ULN) if no demonstrable
             liver metastases or > 5 times ULN in the presence of liver metastases; aspartate
             aminotransferase > 2.5 times ULN if no demonstrable liver metastases or > 5 times ULN
             in the presence of liver metastases

          -  Total bilirubin > 1.5 times ULN if no liver metastases or > 3 times ULN in the
             presence of documented Gilbert's syndrome (unconjugated hyperbilirubinemia) or liver
             metastases

          -  Serum creatinine > 1.5 times ULN concurrent with creatinine clearance < 50 mL/min
             (measured or calculated by Cockcroft and Gault equation)-confirmation of creatinine
             clearance is only required when creatinine is > 1.5 times ULN

          -  Judgment by the investigator that the patient should not participate in the study if
             the patient is unlikely to comply with study procedures, restrictions and requirements