Insect crop pests threaten global food security. This threat is amplified through the spread of nonnative species and through adaptation of native pests to control measures. Adaptations such as pesticide resistance can result from selection on variation within a population, or through gene flow from another population. We investigate these processes in an economically important noctuid crop pest, Helicoverpa zea, which has evolved resistance to a wide range of pesticides. Its sister species Helicoverpa armigera, first detected as an invasive species in Brazil in 2013, introduced the pyrethroid-resistance gene CYP337B3 to South American H. zea via adaptive introgression. To understand whether this could contribute to pesticide resistance in North America, we sequenced 237 H. zea genomes across 10 sample sites. We report H. armigera introgression into the North American H. zea population. Two individuals sampled in Texas in 2019 carry H. armigera haplotypes in a 4 Mbp region containing CYP337B3. Next, we identify signatures of selection in the panmictic population of nonadmixed H. zea, identifying a selective sweep at a second cytochrome P450 gene: CYP333B3. We estimate that its derived allele conferred a ∼5% fitness advantage and show that this estimate explains independently observed rare nonsynonymous CYP333B3 mutations approaching fixation over a ∼20-year period. We also detect putative signatures of selection at a kinesin gene associated with Bt resistance. Overall, we document two mechanisms of rapid adaptation: the introduction of fitness-enhancing alleles through interspecific introgression, and selection on intraspecific variation.