In microorganisms, evolutionarily conserved mechanisms facilitate adaptation to harsh conditions through stress-induced mutagenesis (SIM). Analogous processes may underpin progression and therapeutic failure in human cancer. We describe SIM in multiple in vitro and in vivo models of human cancers under nongenotoxic drug selection, paradoxically enhancing adaptation at a competing intrinsic fitness cost. A genome-wide approach identified the mechanistic target of rapamycin (MTOR) as a stress-sensing rheostat mediating SIM across multiple cancer types and conditions. These observations are consistent with a two-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.