Inclusion Criteria:

          -  Subjects must have histologically confirmed diagnosis of pre-B acute lymphoblastic
             leukemia harboring the t(9;22) translocation (Philadelphia chromosome positive acute
             lymphoblastic leukemia [Ph+ ALL]). All patients must have a bone marrow biopsy
             completed during the screening period. Patients with central nervous system (CNS)
             disease will be included

          -  Newly diagnosed subjects must have received no prior treatment for their ALL with the
             exception of steroids (prednisone, dexamethasone), hydrea or IT methotrexate. Patients
             may receive up to 6 days of pre-treatment with steroids prior to enrollment during the
             screening phase

          -  Patients with relapsed disease may not have had prior treatment with dasatinib

          -  Age >= 18 years. Both men and women and members of all races and ethnic groups will be
             included

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

          -  Must be able to take oral medication

          -  Aspartate aminotransferase (AST) < 2.5 x upper limit of normal (ULN)

               -  Unless considered due to leukemic organ involvement

          -  Alanine aminotransferase (ALT) < 2.5 x ULN

               -  Unless considered due to leukemic involvement

          -  Bilirubin < 1.5 x ULN

               -  Unless considered due to leukemic organ involvement

               -  Note: subjects with Gilbert's Syndrome may have a bilirubin > 1.5 x ULN per
                  discussion between the investigator and AbbVie medical monitor

          -  Subject must have adequate renal function as demonstrated by a calculated creatinine
             clearance >= 50 mL/min; determined via urine collection for 24-hour creatinine
             clearance or by the Cockcroft-Gault formula

               -  NOTE: For subjects that have body mass index (BMI) of > 25 kg/m^2, 24-hour
                  measured creatinine clearance is required

          -  Women of childbearing potential must have a negative serum or urine pregnancy test
             (sensitivity < 25 IU human chorionic gonadotropin [HCG]/L) within 72 hours prior to
             the start of the study drug

          -  Persons of reproductive potential must agree to use an adequate method of
             contraception throughout treatment and for at least 4 weeks after study drug is
             stopped. Women of childbearing potential and men with a sexual partner of childbearing
             potential must be advised of the importance of avoiding pregnancy during trial
             participation and the potential risk factors for an unintentional pregnancy

          -  Normal corrected QT (QTc) interval on screening electrocardiogram (EKG) (< 450 ms in
             men, < 470 ms in women)

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

        Exclusion Criteria:

          -  For newly diagnosed subjects: who have received treatment with cytotoxic chemotherapy,
             radiotherapy or immunotherapy for their ALL, or prior dasatinib treatment. For
             relapsed subjects: prior dasatinib treatment

          -  Subjects who have received any investigational agents or subjects who are taking
             investigational or commercial agents or therapies with the intent to treat the
             subject's malignancy within seven days of enrollment

          -  Subjects with chronic myelogenous leukemia (CML) in myeloid blast crisis, Ph+ acute
             myeloid leukemia (AML) or acute leukemia of ambiguous lineage

          -  Subjects with clinically serious infections as determined by the provider requiring
             ongoing antibiotic therapy. This does not include antibiotic treatment for neutropenic
             fever

          -  Patients with a pleural or pericardial effusion of any grade

          -  Subjects with a history of allergic reactions attributed to compounds of similar
             chemical or biologic composition to dasatinib or other agents used in the study

          -  Subjects who have undergone prior allogeneic hematopoietic stem cell transplantation

          -  Subject has received the following within 7 days prior to the initiation of study
             treatment: Strong or moderate CYP3A inducers (such as rifampin, carbamazepine,
             phenytoin, and St. John's wort); warfarin or inhibitors (such as fluconazole,
             ketoconazole and clarithromycin

          -  Subjects with uncontrolled cardiac illness including but not limited to, symptomatic
             congestive heart failure, unstable angina pectoris, clinically significant ventricular
             arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de
             pointes), or pulmonary hypertension

          -  Subjects with diagnosed congenital prolonged QT syndrome

          -  Pregnant women are excluded from this study because dasatinib is a pregnancy category
             D agent with the potential for teratogenic or abortifacient effects. Because there is
             an unknown but potential risk for adverse events in nursing infants secondary to
             treatment of the mother with dasatinib, breastfeeding should be discontinued if the
             mother is treated with dasatinib. These potential risks may also apply to venetoclax
             for which the pregnancy category and risks to the fetus are unknown

          -  Participant is seropositive with human immunodeficiency virus (HIV) or has active
             infection with hepatitis B virus (HBV) or hepatitis C virus (HCV).

               -  HIV-infected patients on effective anti-retroviral therapy with undetectable
                  viral load within 6 months are eligible for this trial.

               -  For patients with evidence of chronic HBV infection, the HBV viral load must be
                  undetectable on suppressive therapy, if indicated.

               -  Individuals with a history of HCV infection must have been treated and cured. For
                  patients with HCV infection who are currently on treatment, they are eligible if
                  they have an undetectable HCV viral load

          -  Subjects with invasive malignancy over the previous year except treated early stage
             carcinomas of the skin, completely resected intraepithelial carcinoma of the cervix,
             completely resected papillary thyroid and follicular thyroid cancers, and localized
             prostate cancer treated with curative intent with surgery or radiation