Although mechanisms of acquired resistance of epidermal growth factor receptor (EGFR)-mutant non-small-cell lung cancers to EGFR inhibitors have been identified, little is known about how resistant clones evolve during drug therapy. Here we observe that acquired resistance caused by the EGFR^T790M gatekeeper mutation can occur either by selection of pre-existing EGFR^T790M-positive clones or via genetic evolution of initially EGFR^T790M-negative drug-tolerant cells. The path to resistance impacts the biology of the resistant clone, as those that evolved from drug-tolerant cells had a diminished apoptotic response to third-generation EGFR inhibitors that target EGFR^T790M; treatment with navitoclax, an inhibitor of the anti-apoptotic factors BCL-xL and BCL-2 restored sensitivity. We corroborated these findings using cultures derived directly from EGFR inhibitor–resistant patient tumors. These findings provide evidence that clinically relevant drug-resistant cancer cells can both pre-exist and evolve from drug-tolerant cells, and they point to therapeutic opportunities to prevent or overcome resistance in the clinic.