Induction Pembrolizumab and Chemotherapy Followed by Pembrolizumab Before Chemoradiation and Pembrolizumab Maintenance Compared to Standard Chemoradiation With Pembrolizumab Followed by Pembrolizumab Maintenance in High-Risk Cervical Cancer

Inclusion Criteria: * Patients must have pathologically confirmed newly diagnosed cervical cancer. Eligible pathologic types: squamous cell carcinoma, adenocarcinoma, adenosquamous cell carcinoma * Patients must have locally advanced cervical cancer (LACC) with T3 or T4 disease with or without lymph node involvement: * IIIA (T3aN0M0) * IIIB (T3bN0M0) * IIIC1(T3aN1M0, T3bN1M0) * IIIC2 (T3aN2M0, T3bN2M0) * IVA (T4aN0M0, T4aN1M0, T4aN2M0) No prior hysterectomy defined as removal of the entire uterus. * NOTE: prior partial/subtotal hysterectomy for reasons other than cervical cancer are eligible to participate in the study. No plan to perform a hysterectomy as part of initial cervical cancer therapy. No paraaortic lymph node (PALN) metastases above the T12/L1 interspace. * Note: Nodal status can be confirmed by imaging (CT, MRI, or PET/CT), fine needle aspirate/core biopsy, extra peritoneal biopsy, laparoscopic biopsy, or lymphadenectomy. Radiologic definition of lymph node staging: * N1: * One or more pelvic lymph nodes with short axis diameter of ≥ 15 mm (axial plane) by CT or MRI, and/or * One or more pelvic lymph nodes with short axis diameter of ≥ 10 mm and standardized uptake value maximum (SUVmax) ≥ 2.5 by fludeoxyglucose (FDG)-PET * N2: * One or more para-aortic lymph node with short axis diameter of ≥ 15 mm (axial plane) by CT or MRI, and/or * One or more para-aortic lymph node with short axis diameter of ≥ 10 mm and SUVmax ≥ 2.5 by FDG-PET * No prior definitive surgical, radiation, or systemic therapy for cervical cancer * No prior immunotherapy * No prior pelvic radiation therapy for any disease * Age ≥ 18 * Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2 * Not pregnant and not nursing * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm\^3 * Platelets ≥ 100,000 cells/mm\^3 * Hemoglobin ≥ 8 g/dl (Note: The use of transfusion or other intervention to achieve hemoglobulin \[Hgb\] ≥ 8 g/dl is acceptable) * Creatinine clearance (CrCL) of ≥ 50 mL/min by the Cockcroft-Gault formula * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (patients with known Gilbert's disease who have bilirubin level ≤ 3 x institutional ULN may be enrolled) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x institutional ULN * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * No active infection requiring parenteral antibiotics * No live vaccine within 30 days prior to registration. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacille Calmette Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines are live attenuated vaccines and are not allowed * No diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior registration * No active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed * No history of (non-infectious) pneumonitis that required steroids, or current pneumonitis * No history of allergic reaction to the study agent(s) or compounds of similar chemical or biologic composition to the study agent(s) (or any of its excipients)