Inclusion Criteria:
* Ability to understand and willingness to sign an IRB-approved informed consent.
* Age ≥ 18 years at the time of consent.
* ECOG Performance Status (PS) ≤ 2.
* Histological or cytological confirmation of newly diagnosed CD19-positive Philadelphia-chromosome/BCR::ABL1-positive ALL.
* Creatinine clearance: ≥60 mL/min, determined by the Cockroft-Gault formula, or measured by a 24-hour urine collection.
* Bilirubin ≤ 1.5 × upper limit of normal (ULN) - Unless liver abnormalities considered due to Gilbert's syndrome or of non-hepatic origin i.e., leukemic involvement. For patients with Gilbert's syndrome, bilirubin ≤1.5 x of their baseline bilirubin level will be required.
* Aspartate aminotransferase (AST) - Unless liver abnormalities considered due to Gilbert's syndrome or of non-hepatic origin i.e., leukemic involvement. For patients with Gilbert's syndrome, bilirubin ≤1.5 x of their baseline bilirubin level will be required.
* Alanine aminotransferase (ALT) - Unless liver abnormalities considered due to Gilbert's syndrome or of non-hepatic origin i.e., leukemic involvement. For patients with Gilbert's syndrome, bilirubin ≤1.5 x of their baseline bilirubin level will be required.
* Individuals of childbearing potential (ICBP) must have a negative serum pregnancy test. NOTE: Individuals who may become pregnant are considered to have childbearing potential unless they are surgically infertile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are postmenopausal (at least 12 consecutive months with no menses without an alternative medical cause).
* ICBP must be willing to use two forms of contraception, one of which must be a barrier method and the other must be a highly effective contraceptive method from the time of informed consent until 6 months after study treatment discontinuation. Male participants with female partners of reproductive potential will need to agree to use contraception methods described above during study treatment and for at least 6 months after completion of all study treatment.
* Male participants must agree to refrain from sperm donation during study treatment and for at least 6 months after completion of all study treatment.
* Ability to ingest oral medications without a malabsorption condition, known dysphagia, short-gut syndrome, gastroparesis, or other conditions that may limit the ingestion or gastrointestinal absorption, distribution, metabolism and excretion of drugs administered orally, per the enrolling investigator.
Exclusion Criteria:
* Any prior treatment for ALL except for a single dose of intrathecal (IT) chemotherapy, corticosteroids, hydroxyurea, a single dose of vincristine, cytarabine, leukapheresis, and/or a BCR::ABL1-targeted tyrosine kinase inhibitor. Permitted prior treatment is limited to a duration of no longer than 14 days. Permitted prior treatment must be stopped at least 24 hours prior to starting study therapy.
* Women who are pregnant, nursing, or who plan to become pregnant while in the study and for at least 6 months after the last administration of all study treatment. NOTE: breast milk cannot be stored for future use while the mother is being treated on study. Pregnant participants are excluded from this study because ponatinib, blinatumomab, and methotrexate have 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 ponatinib, blinatumomab, and methotrexate breastfeeding should be discontinued if the patient is treated with ponatinib, blinatumomab, and methotrexate.
* Active second malignancy except for localized prostate cancer, basal cell or squamous cell carcinoma of the skin and carcinoma in situ of the skin or cervix.
* Unstable or severe uncontrolled medical condition in the opinion of the enrolling investigator (e.g., unstable cardiac function or unstable pulmonary condition; uncontrolled infection).
* Participants with known history of hepatitis B virus, hepatitis C virus, or human immunodeficiency virus (HIV) are eligible if no evidence of active viral replication by blood testing (i.e. negative viral loads). HIV positive participants must be on active anti-retroviral therapy and willing to continue therapy during study treatment.
* Uncontrolled cardiac disease as determined by the enrolling investigator.
* Major surgery, as determined by the enrolling investigator, within 2 weeks before enrollment.