Essential epigenetic dependencies have become evident in many cancers. Based on the functional antagonism between BAF/SWI/SNF and PRC2 in SMARCB1-deficient sarcomas, we and colleagues recently completed the clinical trial of the EZH2 inhibitor tazemetostat. However, the principles of tumor response to epigenetic therapy in general, and tazemetostat in particular, remain unknown. Using functional genomics of patient tumors and diverse experimental models, we sought to define molecular mechanisms of tazemetostat resistance in SMARCB1-deficient sarcomas and rhabdoid tumors. We found distinct classes of acquired mutations that converge on the RB1/E2F axis and decouple EZH2-dependent differentiation and cell cycle control. This allows tumor cells to escape tazemetostat-induced G1 arrest despite EZH2 inhibition, and suggests a general mechanism for effective EZH2 therapy. This also enables us to develop combination strategies to circumvent tazemetostat resistance using cell cycle bypass targeting via AURKB, and synthetic lethal targeting of PGBD5-dependent DNA damage repair via ATR. This reveals prospective biomarkers for therapy stratification, including PRICKLE1 associated with tazemetostat resistance. In all, this work offers a paradigm for rational epigenetic combination therapy suitable for immediate translation to clinical trials for epithelioid sarcomas, rhabdoid tumors, and other epigenetically dysregulated cancers.