Here we aim to test the notion that overcoming cancer cells’ acquired resistance to chemotherapy drugs may be achieved by administrating together with the main drug a molecule that is not toxic by itself but enhances the drug efficacy in killing the resistant cells. Finding such a supplementary molecule is a nontrivial task. Our algorithmic approach, named OVERcoming Drug Resistance by In Vitro cell Exposure (OVERDRIVE), involves exposing drug-sensitive cancer cells to increasing drug concentrations for several weeks followed by a comprehensive proteomic analysis of both the exposed and sensitive cells. Applying a machine learning tool Genome Enhancer to the proteomic data reveals the protein network accounting for the differences between the exposed and naïve cells and predicts molecules that may shift the exposed cell phenotypes to the sensitive one. Experimental validation of the top predicted nontoxic molecules confirmed that the combined treatment of the experimental drug LTCA2940 that targets redox pathways with identified supplementary molecule restored the sensitivity of LTCA2940-resistant cells. The OVERDRIVE approach may pave a way for a strategy to overcoming anticancer resistance to chemotherapy in clinic.