The emergence of resistance to cancer therapy remains a pressing challenge and has led to several major experimental efforts aiming to identify individual molecular signatures of resistance to specific cancer drugs. Here we describe a comprehensive computational framework for identifying the molecular pathways underlying cancer resistance, accounting for many of these results. Our approach, termed INCISOR, is applied to mine The Cancer Genome Atlas (TCGA), a large collection of cancer patients’ data, to identify a class of genetic interactions termed synthetic rescues (SR). An SR denotes a functional interaction between two genes where a change in the activity of one vulnerable gene (which may be a target of a cancer drug) is lethal but the subsequent altered activity of its partner rescuer gene restores cell viability. Applying INCISOR to the TCGA identifies the first pan-cancer SR networks, composed of interactions common to many cancer types. We experimentally test and validate a subset of these interactions involving the master regulator gene mTOR. We find that rescuer genes become increasingly activated as breast cancer progresses, testifying to pervasive ongoing rescue processes. We show that SRs can be utilized to successfully predict patients’ survival and response to the majority of current cancer drugs, and importantly, for predicting the emergence of drug resistance from the initial tumor biopsy. Our analysis suggests a potential new strategy for enhancing the effectiveness of existing cancer therapies by targeting their rescuer genes to counteract resistance.