Testing the Addition of Paclitaxel and Carboplatin Given After Standard Chemotherapy and Radiation for Cervical Cancer in HIV-positive Women

This trial will be conducted at selected AIDS Malignancy Consortium sites in Sub-Saharan Africa. Eligibility Criteria for Screening * Ability to understand and the willingness to provide informed consent. * Participant has clinically diagnosed LACC and self-reports as HIV-positive * Age ≥ 18 years. DOB and age will be determined based on best possible information or documentation available. * ECOG performance status ≤ 2 (Karnofsky ≥ 50%, see Appendix III). Inclusion Criteria for chemoradiation treatment enrollment: * Participants with locally advanced primary, untreated, histologically-confirmed, documented invasive squamous cell carcinoma, adenocarcinoma, or adenosquamous carcinoma of the uterine cervix, adequately clinically staged by standard clinical guidelines, with Federation of Gynecology and Obstetrics (FIGO) stages IIB, III, or IVA * HIV positive. Documentation of HIV-1 infection by means of any one of the following: * Documentation of receipt of ART by a licensed health care provider (documentation may be a record of an ART prescription in the participant's medical record, a written prescription in the name of the participant for ART, or pill bottles for ART with a label showing the participant's name) * HIV-1 ribonucleic acid (RNA) detection by a licensed HIV-1 RNA assay demonstrating \>1000 RNA copies/mL confirmed by a licensed screening antibody and/or HIV antibody antigen combination assay * Any licensed HIV screening antibody and/or HIV antibody/antigen combination assay confirmed by a second licensed HIV assay such as a HIV-1 Western blot confirmation or HIV rapid multispot antibody differentiation assay. * Note: The term "licensed" refers to a kit that has been certified or licensed by an oversight body within the participating country and validated internally. WHO (World Health Organization) and CDC (Centers for Disease Control and Prevention) guidelines mandate that confirmation of the initial test result must use a test that is different from the one used for the initial assessment. A reactive initial rapid test should be confirmed by either another type of rapid assay or an E/CIA that is based on a different antigen preparation and/or different test principle (e.g., indirect versus competitive), or a Western blot or a plasma HIV-1 RNA viral load. * Hemoglobin \>= 10 g/dL (6.2 mmol/L) (participants receiving transfusion are permitted) (within 4 weeks prior to enrollment) * Leukocytes: \>= 3,000/mm\^3 (3.0 x 10\^9/L) (within 4 weeks prior to enrollment) * Absolute neutrophil count: \>= 1,500/mm\^3 (1.5 x 10\^9/L) (within 4 weeks prior to enrollment) * Platelets: \>= 100,000/mm\^3 (100 x 10\^9/L) (within 4 weeks prior to enrollment) * CD4 T-cell count a minimum of 200 cells/uL (within 4 weeks prior to enrollment) * Total bilirubin =\< 2 x institutional upper limit of normal (ULN) unless related to antiretroviral use (e.g., atazanavir or indinavir), then the direct bilirubin must be =\< 2 x ULN (within 4 weeks prior to enrollment) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]): =\< 3 x ULN (within 4 weeks prior to enrollment) * Creatinine levels within normal institutional limits or, creatinine clearance \>= 60 mL/min/1.73 m\^2 (1.00 mL/s) calculated by the Cockcroft-Gault equation for women for participants with creatinine levels above institutional normal (within 4 weeks prior to enrollment) * All participants must be prescribed combination antiretroviral therapy with the goal of virological suppression using an acceptable regimen that adheres to national guidelines for treatment of HIV infection. If on a ritonavir- or cobicistat-based regimen, the participant must be switched to a non-ritonavir/ cobicistat-based regimen at least 7 days before treatment enrollment. Participants not on ART must start an acceptable regimen at least 7 days before treatment enrollment. * In the investigator's opinion the participant is suitable for treatment with radical intent using concurrent chemotherapy and pelvic radiation followed by adjuvant chemotherapy * Participants of childbearing potential, defined as a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months), must have a negative urine or serum pregnancy test within 3 weeks prior to enrollment and agree to use an effective form of contraception (e.g., barrier contraception, highly effective hormonal contraception) for the duration of treatment and for 6 weeks after stopping treatment * Life expectancy of greater than 6 months Exclusion Criteria for chemoradiation treatment enrollment: * Participants who have had chemotherapy for cervical cancer within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study * Participants who are receiving any other investigational agents * Participants who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicity \> grade 1). * Participants who have undergone hysterectomy including supracervical hysterectomy * Acute active (such as tuberculosis or malaria), serious, uncontrolled infection * Prior invasive malignancy requiring systemic chemotherapy diagnosed within the past 24 months (other than LACC) * A medical or psychiatric illness that precludes ability to give informed consent or is likely to interfere with the ability to comply with the protocol stipulations * Participants with circumstances that will not permit completion of the study or required follow-up. For instance, if travel to and from treatment site is an issue * Participants with carcinoma of the cervical stump * Participants with history of cardiovascular disease manifested as: * History of myocardial infarction * Unstable angina * Currently taking medication for treatment of angina * History of coronary artery bypass surgery * New York Heart Association class 3 or 4 heart failure * Participants with enlarged para-aortic lymph node involvement above L3 on imaging that are suspicious for metastasis * History of allergic reactions attributed to compounds of similar chemical or biological composition to study drugs (cisplatin, carboplatin, and paclitaxel) * Participants who are breastfeeding a child. Cisplatin is known to be excreted in human milk. Eligibility for Randomization * Participants must have organ and marrow function within the following parameters within 4-8 weeks post CDDP/RT to be eligible for randomization * Absolute neutrophil count: ≥1,500/mm3 (1.5 x 109/L) * Platelets: ≥ 100,000/mm3 (100 x 109/L) * CD4 T-cell \> 100 cells/µL * HIV viral load \< 400 copies/mL * ECOG performance status ≤ 2 (Karnofsky ≥ 50%). * Successful completion of CDDP/RT, defined as receiving 4-6 cycles of cisplatin and completion of the equivalent dose per fraction of \>78 Gy to Point A.