APOBEC mutagenesis is one of the most common endogenous sources of mutations in human cancer and is a major source of genetic intratumor heterogeneity. High levels of APOBEC mutagenesis are associated with poor prognosis and aggressive disease across diverse cancers, but the mechanistic and functional impacts of APOBEC mutagenesis on tumor evolution and therapy resistance remain relatively unexplored. To address this, we investigated the contribution of APOBEC mutagenesis to acquired therapy resistance in a model of EGFR-mutant non-small cell lung cancer. We find that inhibition of EGFR in lung cancer cells leads to a rapid and pronounced induction of APOBEC3 expression and activity. Functionally, APOBEC expression promotes the survival of drug-tolerant persister cells (DTPs) following EGFR inhibition. Constitutive expression of APOBEC3B alters the evolutionary trajectory of acquired resistance to the EGFR inhibitor gefitinib, making it more likely that resistance arises through de novo acquisition of the T790M gatekeeper mutation and squamous transdifferentiation during the DTP state. APOBEC3B expression is associated with increased expression of the squamous cell transcription factor ΔNp63 and squamous cell transdifferentiation in gefitinib-resistant cells. Knockout of p63 in gefitinib-resistant cells reduces the expression of the ΔNp63 target genes IL1α/β and sensitizes these cells to the third-generation EGFR inhibitor osimertinib. These results suggest that APOBEC activity promotes acquired resistance by facilitating evolution and transdifferentiation in DTPs, and suggest that approaches to target ΔNp63 in gefitinib-resistant lung cancers may have therapeutic benefit.