Drug resistance results in poor outcomes for cancer patients. Adaptive therapy is a potential strategy to address drug resistance that exploits competitive interactions between sensitive and resistant subclones. Here, we showed that adapting carboplatin dose according to tumor response (adaptive therapy) significantly prolonged survival of murine ovarian cancer models compared to standard carboplatin dosing, without increasing mean daily drug dose or toxicity. Platinum resistant ovarian cancer cells exhibited diminished fitness when drug was absent in vitro and in vivo, which caused selective decline of resistant populations due to reduced proliferation and increased apoptosis. Conversely fitter, sensitive cells re-grew when drug was withdrawn. Using a bioinformatics pipeline that exploits copy number changes to quantify the emergence of treatment resistance, analysis of cell-free DNA obtained longitudinally from ovarian cancer patients during treatment showed subclonal selection through therapy, and measurements of resistant population growth correlated strongly with disease burden. These preclinical findings pave the way for future clinical testing of personalized adaptive therapy regimens tailored to the evolution of carboplatin resistance in individual ovarian cancer patients.