The remarkable biological and evolutionary adaptations of insects to plants are largely attributed to the powerful chemosensory systems of insects. The tomato leaf miner (Tuta absoluta) is a destructive invasive pest with a global distribution that poses a serious threat to the production of nightshade crops, especially tomatoes. Functional plants can attract or repel insect pests by releasing volatiles that interact with the olfactory system of insects, thereby reducing the damage of insect pests to target crops. However, there is limited research on the interaction between T. absoluta olfactory genes and functional plants. In this study, 97 members of the putative odorant-binding protein (OBP) family have been identified in the whole genome of T. absoluta. Phylogenetic analysis involving various Lepidopteran and Dipteran species, including D. melanogaster, revealed that OBP gene families present conserved clustering patterns. Furthermore, the Plus-C subfamily of OBP showed extremely significant expansion. Moreover, the expression levels of the OBP genes varied significantly between different developmental stages; that is, the highest number of OBP genes were expressed in the adult stage, followed by the larval stage, and fewer genes were expressed in high abundance in the egg stage. On the other hand, through a Y-tube olfactometer, we identified a functional plant—Plectranthus tomentosa—that significantly repels adult and larval T. absoluta. Finally, we screened the OBP genes in response to tomato and P. tomentosa volatiles at the genomic level of T. absoluta using RT-qPCR. These results laid a good foundation for controlling T. absoluta with functional plants and further studying olfactory genes.