Abstract Epigenetic dependencies have become evident in many cancers. On the basis of antagonism between BAF/SWI-SNF and PRC2 in SMARCB1-deficient sarcomas, we 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 and diverse experimental models, we define molecular mechanisms of tazemetostat resistance in SMARCB1-deficient tumors. We found distinct 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, suggests a general mechanism for effective therapy, and provides prospective biomarkers for therapy stratification, including PRICKLE1. On the basis of this, we develop a combination strategy to circumvent tazemetostat resistance using bypass targeting of AURKB. This offers a paradigm for rational epigenetic combination therapy suitable for translation to clinical trials for epithelioid sarcomas, rhabdoid tumors, and other epigenetically dysregulated cancers. Significance: Genomic studies of patient epithelioid sarcomas and rhabdoid tumors identify mutations converging on a common pathway for response to EZH2 inhibition. Resistance mutations decouple drug-induced differentiation from cell-cycle control. We identify an epigenetic combination strategy to overcome resistance and improve durability of response, supporting its investigation in clinical trials. See related commentary by Paolini and Souroullas, p. 903. This article is featured in Selected Articles from This Issue, p. 897