In micro-organisms, evolutionarily conserved mechanisms facilitate adaptation to harsh conditions via stress-induced mutagenesis (SIM). Analogous mechanisms may underpin progression and therapeutic failure in human cancer. Here, we describe SIM in multiple cancer types under non-genotoxic drug selection, paradoxically enhancing adaptation at a competing intrinsic fitness cost. A genome-wide approach identified MTOR as a stress-sensing rheostat mediating SIM across multiple cancer types and conditions. These observations are consistent with a 2-phase model for drug resistance, in which an initially rapid expansion of genetic diversity is counterbalanced by an intrinsic fitness penalty, subsequently normalizing to complete adaptation under the new conditions. This model suggests synthetic lethal strategies to minimize resistance to anticancer therapy.