Therapy resistance is a major challenge in the treatment of cancer. Here, we performed CRISPR-Cas9 screens across a broad range of therapies used in acute myeloid leukemia to identify genomic determinants of drug response. Our screens uncover a selective dependency on RNA splicing factors whose loss preferentially enhances response to the BCL2 inhibitor venetoclax. Loss of the splicing factor RBM10 augments response to venetoclax in leukemia yet is completely dispensable for normal hematopoiesis. Combined RBM10 and BCL2 inhibition leads to mis-splicing and inactivation of the inhibitor of apoptosis XIAP and downregulation of BCL2A1, an anti-apoptotic protein implicated in venetoclax resistance. Inhibition of splicing kinase families CLKs (CDC-like kinases) and DYRKs (dual-specificity tyrosine-regulated kinases) leads to aberrant splicing of key splicing and apoptotic factors that synergize with venetoclax, and overcomes resistance to BCL2 inhibition. Our findings underscore the importance of splicing in modulating response to therapies and provide a strategy to improve venetoclax-based treatments.