Most targeted cancer therapies fail to achieve complete tumor regressions or attain durable remissions. To understand why these treatments fail to induce robust cytotoxic responses despite appropriately targeting oncogenic drivers, here we systematically interrogated the dependence of cancer cells on the BCL-2 family of apoptotic proteins after drug treatment. We observe that multiple targeted therapies, including BRAF or EGFR inhibitors, rapidly deplete the pro-apoptotic factor NOXA, thus creating a dependence on the anti-apoptotic protein MCL-1. This adaptation requires a pathway leading to destabilization of the NOXA mRNA transcript. We find that interruption of this mechanism of anti-apoptotic adaptive resistance dramatically increases cytotoxic responses in cell lines and a murine melanoma model. These results identify NOXA mRNA destabilization/MCL-1 adaptation as a non-genomic mechanism that limits apoptotic responses, suggesting that sequencing of MCL-1 inhibitors with targeted therapies could overcome such widespread and clinically important resistance.