Temozolomide and Irinotecan Hydrochloride With or Without Bevacizumab in Treating Young Patients With Recurrent or Refractory Medulloblastoma or CNS Primitive Neuroectodermal Tumors

Inclusion Criteria: * Medulloblastoma or PNET of childhood that has relapsed or become refractory to standard chemotherapy; patients with pineoblastoma are eligible * Patients must have had histologic verification of the malignancy at original diagnosis or at the time of recurrence * Patients must have clear residual disease, defined as tumor that is measurable in two perpendicular diameters on magnetic resonance imaging (MRI) OR diffuse leptomeningeal disease OR clear MRI evidence of disease that may not be measurable in two perpendicular diameters * All patients must have a brain MRI with and without gadolinium and a spine MRI with gadolinium performed within 2 weeks prior to study enrollment * Patients must have a Lansky or Karnofsky performance status score of \>= 50%, corresponding to Eastern Cooperative Oncology Group (ECOG) categories of 0, 1, or 2 (use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age) * Patients must have a life expectancy of \>= 8 weeks * Patients must have experienced at least one and at most two relapses prior to study enrollment; patients with primary refractory disease are eligible * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study * Myelosuppressive chemotherapy: Must not have received within 3 weeks of entry onto this study (6 weeks if prior nitrosourea) * Biologic (anti-neoplastic agent): At least 7 days since the completion of therapy with a biologic agent; at least 3 weeks for biologic agents with a long half life, such as antibodies * External beam radiation therapy (XRT): Must not have received craniospinal radiotherapy within 24 weeks prior to study entry; the tumor designated as "measurable" for protocol purposes must not have received radiation within 12 weeks prior to study entry); focal radiation to areas of symptomatic metastatic disease must not be given within 14 days of study entry * Stem cell transplant (SCT): For autologous SCT, \>= 3 months must have elapsed prior to study entry * Study specific limitations on prior therapy: * Patients must not have previously received bevacizumab, irinotecan, temozolomide or other anti-vascular endothelial growth factor (VEGF) inhibitor * Patients must not be taking enzyme-inducing antiepileptic medicines within 1 week of study entry * Patients must have recovered from any surgical procedure before enrolling on this study: * Patients with a major surgical procedure within 28 days prior to enrollment should be excluded * Patients with an intermediate surgical procedure within 14 days prior to enrollment should be excluded * For minor surgical procedures (including Broviac line or infusaport placement), patients should not receive the first planned dose of bevacizumab until the wound is healed and at least 7 days have elapsed * There should be no anticipation of need for major surgical procedures during the course of the study * Examples of major, intermediate, or minor surgical procedures: * Major procedures: Major craniotomy for tumor resection; organ resection; bowel wall anastomosis; arteriovenous grafts; exploratory laparotomy; thoracotomy * Intermediate procedures: Ventriculoperitoneal (VP)-shunt placement; stereotactic brain biopsy * Minor procedures: Incision and drainage of superficial skin abscesses; punch biopsy of skin lesions; superficial skin wound suturing; bone marrow aspirate and/or biopsy; fine needle aspirations; Broviac line or infusaport placement; paracentesis or thoracocentesis * Please note: Lumbar punctures or placement of peripherally inserted central catheter (PICC) lines are not considered minor procedures and may occur at any time prior to or during therapy * Hypertension must be well controlled (=\< 95th percentile for age and height if patient is =\< 17 years) on stable doses of medication * Concomitant medications restrictions: * Growth factor(s): Must not have received within 7 days of entry onto this study * Steroids: Patients who are receiving corticosteroids must be on a stable or decreasing dose for at least 7 days * Study Specific: Patients must not be currently taking nonsteroidal anti-inflammatory drugs (NSAIDs), clopidrogel, dipyridamole or aspirin therapy \> 81 mg/day * Peripheral absolute neutrophil count (ANC) \>= 1000/uL (must not have received filgrastim \[G-CSF\] within the prior 7 days) * Platelet count \>= 100,000/uL (transfusion independent) * Hemoglobin \>= 8.0 gm/dL (may receive packed red blood cell \[PRBC\] transfusions) * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min OR a serum creatinine based on age/gender as follows: * =\< 0.4 mg/dL (for patients aged 1 month to \< 6 months) * =\< 0.5 mg/dL (for patients aged 6 months to \< 1 year) * =\< 0.6 mg/dL (for patients aged 1 to \< 2 years) * =\< 0.8 mg/dL (for patients aged 2 to \< 6 years) * =\< 1 mg/dL (for patients aged 6 to \< 10 years) * =\< 1.2 mg/dL (for patients aged 10 to \< 13 years) * =\< 1.4 mg/dL (for female patients aged \>= 13 years) * =\< 1.5 mg/dL (for male patients aged 13 to \< 16 years) * =\< 1.7 mg/dL (for male patients aged \>= 16 years) * Urine protein should be screened by dipstick analysis; if protein \>= 2+ on dipstick, then urine protein creatinine (UPC) ratio should be calculated; if UPC ratio \> 0.5, 24-hour urine protein should be obtained and the level should be \< 1000 mg/24 hours for patient enrollment * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 3 x upper limit of normal (ULN) for age * Central nervous system function defined as * Patients with a seizure disorder may be enrolled if well-controlled and on non-enzyme inducing anticonvulsants * Adequate coagulation defined as * International normalized ratio (INR)/prothrombin time (PT) =\< 1.5 x upper limit of normal Exclusion Criteria: * Patients with a serious or non-healing wound, ulcer, or bone fracture are not eligible for this study * Patients must not have a history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 6 months prior to study entry * Patients must not have a known bleeding diathesis or coagulopathy * Patients must not have had significant vascular disease (eg, aortic aneurysm requiring surgical repair, deep venous or arterial thrombosis) within the last 6 months prior to study entry * Patients must not have a known thrombophilic condition (i.e. protein S, protein C or antithrombin III deficiency, Factor V Leiden, Factor II G20210A mutation, homocysteinemia or antiphospholipid antibody syndrome); testing is not required in patients without thrombophilic history * Patients must not have evidence of new CNS hemorrhage on baseline MRI obtained within 14 days prior to study enrollment * Patients with a history of stroke, myocardial infarction, transient ischemic attack (TIA), severe or unstable angina, peripheral vascular disease, or grade II or greater congestive heart failure within the past 6 months are not eligible * Patients must not have serious and inadequately controlled cardiac arrhythmia * Female patients who are pregnant are not eligible for this study * Female patients who are breastfeeding are not eligible for this study unless they agree not to breastfeed * Female patients of childbearing potential must have a negative pregnancy test * Sexually active patients of childbearing potential must agree to use an effective method of contraception during the study and for at least 6 months after the completion of bevacizumab therapy * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies