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.