• Patients must be \>= 1 and \< 31 years at time of enrollment

• Patients must have first relapse of CD19+ B-ALL (relapse blasts must express CD19) in one of the following categories:

‣ Isolated bone marrow relapse

⁃ Isolated central nervous system (CNS) (excluding known optic nerve/retinal and CNS chloromas) and/or testicular relapse

⁃ Combined bone marrow with extramedullary relapse in the CNS (excluding known optic nerve/retinal and CNS chloromas) and/or testes

• Patients with Down syndrome (DS) are eligible in the following categories:

‣ Isolated bone marrow relapse

⁃ Combined bone marrow with CNS (excluding known optic nerve/retinal and CNS chloromas) and/or testicular relapse

• Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2. Use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age

‣ Of note, for patients with developmental delay (e.g., Down syndrome) regardless of age, Lansky scale may be substituted for Karnofsky scale. However, the requirement for ECOG 0-2 remains, regardless of known history of developmental delay

• Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study

‣ Patients with prior blinatumomab or CD19+ chimeric antigen receptor therapy in the upfront setting will be eligible, provided relapsed lymphoblasts retain CD19 expression

⁃ Patients must not have had a prior hematopoietic stem cell transplant

⁃ A single intrathecal chemotherapy at the time of relapse will be allowed. If \< 7 days have elapsed between this intrathecal therapy (IT) and the start of protocol therapy, then the day 1 intrathecal chemotherapy (i.e. methotrexate, cytarabine, or triple intrathecal) may be omitted

⁃ In the 28 days prior to enrollment, up to five days of post-relapse, pre-enrollment therapy (steroids and/or hydroxyurea only) is permissible

• Patients with Down syndrome who received pre-enrollment therapy and have a white blood count (WBC) \>= 30,000/ul at the time of enrollment still must receive protocol specified cytoreductive therapy with vincristine and dexamethasone, and no washout is required

∙ Patients with Down syndrome who received pre-enrollment therapy and have a WBC \< 30,000/ul at the time of enrollment must be given a 24 hour washout before starting immunotherapy

⁃ Note: There is no waiting period or washout for patients who relapse while receiving upfront therapy

• Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 OR a serum creatinine based on age/sex as follows (within 7 calendar days prior to enrollment):

‣ Age: Maximum serum creatinine (mg/dL)

• 1 to \< 2 years: 0.6 (male), 0.6 (female)

∙ \>= 16 years: 1.7 (male), 1.4 (female)

⁃ The threshold creatinine values in this Table were derived from the Schwartz formula for estimating GFR utilizing child length and stature data published by the Center for Disease Control (CDC)

• Shortening fraction of \>= 27% by echocardiogram, or ejection fraction of \>= 50% by echocardiogram, cardiac magnetic resonance imaging (MRI) or radionuclide angiogram

• No evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \> 94% if there is clinical indication for determination

• All patients and/or their parents or legal guardians must sign a written informed consent

• All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met