Imatinib Mesylate and Combination Chemotherapy in Treating Patients With Newly Diagnosed Philadelphia Chromosome Positive Acute Lymphoblastic Leukemia

Inclusion Criteria: * For patients enrolled on APEC14B1 prior to enrollment on AALL1631, the required diagnostic bone marrow sample has been fulfilled * For patients who have not previously enrolled on APEC14B1 prior to enrollment on AALL1631, a baseline diagnostic sample (or peripheral blood sample with blasts if marrow sample unavailable) must be available to develop an MRD probe * In addition, laboratory reports detailing evidence of BCR::ABL1 fusion or ABL-class fusion must be submitted for rapid central review within 72 hours of study enrollment * \>= 1 year (365 days) and =\< 21 years at ALL diagnosis * Ph+ (BCR::ABL1 fusion): newly diagnosed de novo ALL (B-ALL or T-ALL) or mixed phenotypic acute leukemia (MPAL meeting 2016 World Health Organization \[WHO\] definition) with definitive evidence of BCR::ABL1 fusion by karyotype, fluorescence in situ hybridization (FISH) and/or molecular methodologies * ABL-class fusion: newly diagnosed B-ALL with definitive evidence of ABL-class fusions. ABL-class fusions are defined as those involving the following genes: ABL1, ABL2, CSF1R, PDGFRB, PDGFRA. Methods of detection include fluorescence in-situ hybridization (\[FISH\], e.g. using break-apart or colocalization signals probes), multiplex or singleplex reverse-transcription polymerase chain reaction (RT-PCR), whole transcriptome or panel-based RNA-sequencing (e.g. TruSight RNA Pan-Cancer Panel; Illumina, San Diego, California \[CA\], United States of America \[USA\] or similar) * Ph+ patients must have previously started Induction therapy, which includes vincristine, a corticosteroid, pegaspargase, with or without anthracycline, and/or other standard cytotoxic chemotherapy * Ph+ patients have not received more than 14 days of multiagent Induction therapy beginning with the first dose of vinCRIStine * Ph+ patients may have started imatinib prior to study entry but have not received more than 14 days of imatinib * ABL-class fusion patients must have previously completed the 4 or 5 weeks of multiagent Induction chemotherapy (Induction IA phase) * ABL-class fusion patients may have started imatinib during Induction IA, at the same time of or after the first vinCRIStine dose * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1, or 2 * Direct bilirubin =\< 2.0 mg/dL * Shortening fraction of \>= 27% by echocardiogram * Ejection fraction of \>= 50% by radionuclide angiogram or echocardiogram * Corrected QT interval, QTc \< 480 msec * Note: Repeat echocardiogram and electrocardiogram are not required if they were performed at or after initial ALL diagnosis, before study enrollment * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or serum creatinine within normal limits based on age/gender, as follows: * 1 to \< 2 years: maximum serum creatinine 0.6 mg/dL (both male and female) * 2 to \< 6 years: maximum serum creatinine 0.8 mg/dL (both male and female) * 6 to \< 10 years: maximum serum creatinine 1 mg/dL (both male and female) * 10 to \< 13 years: maximum serum creatinine 1.2 mg/dL (both male and female) * 13 to \< 16 years: maximum serum creatinine 1.5 mg/dL (male), 1.4 mg/dL (female) * \>= 16 years: maximum serum creatinine 1.7 mg/dL (male), 1.4 mg/dL (female) Exclusion Criteria: * Known history of chronic myelogenous leukemia (CML) * ALL developing after a previous cancer treated with cytotoxic chemotherapy * Active, uncontrolled infection, or active systemic illness that requires ongoing vasopressor support or mechanical ventilation * Down syndrome * Pregnancy and breast feeding * Female patients who are pregnant since fetal toxicities and teratogenic effects have been noted for several of the study drugs. A pregnancy test is required for female patients of childbearing potential * Lactating females who plan to breastfeed their infants * Sexually active patients of reproductive potential who have not agreed to use an effective contraceptive method for the duration of treatment according to protocol * Patients with congenital long QT syndrome, history of ventricular arrhythmias or heart block * Prior treatment with dasatinib, or any TKI other than imatinib