Chemoradiation Therapy and Ipilimumab in Treating Patients With Stages IB2-IIB or IIIB-IVA Cervical Cancer

Inclusion Criteria: * Patients with histologically confirmed advanced cervical cancer (squamous cell carcinoma, adenocarcinoma, and adenosquamous cell carcinoma): International Federation of Gynecology and Obstetrics (FIGO) clinical stages IB2/IIA with positive para-aortic lymph nodes or FIGO clinical stages IIB/IIIB/IVA with positive pelvic and/or para-aortic lymph nodes; nodal status will be confirmed by PET/CT scan, fine needle biopsy, extra peritoneal biopsy, laparoscopic biopsy or lymphadenectomy * Patients must have a Gynecologic Oncology Group (GOG) performance status of 0-1 * Absolute neutrophil count (ANC) \>= 1,500/mcl * Platelets \>= 100,000/mcl * Creatinine =\< institutional upper limit normal (ULN); note: if creatinine \> ULN, creatinine clearance must be \> 50 mL/min * Bilirubin =\< 1.5 x ULN * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN * Alkaline phosphatase =\< 2.5 x ULN * Neuropathy (sensory and motor) =\< grade 1 * Patients with ureteral obstruction (i.e., hydronephrosis identified on CT imaging) must undergo stent or nephrostomy tube placement prior to study entry * Patients must meet the pre-entry requirements specified * Patients must have signed an approved informed consent and authorization permitting the release of personal health information * Patients of child-bearing potential must have a negative serum pregnancy test prior to study entry (within 72 hours prior to initiation of study treatment) and be practicing an effective form of contraception; women should not breast-feed while on this study * Patients must not be receiving any other investigational agent * Patients should have an audiogram at baseline, and patients with pre-existing hearing loss or hearing loss during treatment should be assessed frequently during cisplatin therapy Exclusion Criteria: * Patients who have received previous pelvic or abdominal radiation, cytotoxic chemotherapy, or previous therapy of any kind for this malignancy or any pelvic or abdominal radiation for any prior malignancy * Patients with active infection * Patients who have circumstances that will not permit completion of this study or the required follow-up * Patients with renal abnormalities, such as pelvic kidney, horseshoe kidney, or renal transplantation, that would require modification of radiation fields * Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancer, are excluded if there is any evidence of other malignancy being present within the last five years; patients are also excluded if their previous cancer treatment prevents full delivery of this protocol therapy * Patients who have undergone major surgery, excluding diagnostic biopsy, within 30 days (to allow for full recovery) prior to registration * Patients who have a significant history of cardiac disease, i.e., uncontrolled hypertension, unstable angina, congestive heart failure, or uncontrolled arrhythmias within 6 months of registration * Patients with a history of prior treatment with ipilimumab, anti-programmed cell death (PD) 1 antibody, cluster of differentiation (CD)137 agonist or other immune activating therapy such as anti-CD 40 antibody * Patients who are receiving any other investigational agents * Autoimmune disease: patients with a history of inflammatory bowel disease, including ulcerative colitis and Crohn's disease, are excluded from this study, as are patients with a history of symptomatic disease (e.g., rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[e.g., Wegener's Granulomatosis\]); central nervous system (CNS) or motor neuropathy considered of autoimmune origin (e.g. Guillain-Barre syndrome and myasthenia gravis, multiple sclerosis) * Patients with known immune impairment who may be unable to respond to anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA 4) antibody * History of allergic reactions attributed to compounds of similar chemical or biologic composition ipilimumab or other agents used in study * Patients with chronic human immunodeficiency virus (HIV), hepatitis B or hepatitis C infections should be excluded