<p>Pre-existing mutations can influence subsequent evolution by constraining or opening evolutionary pathways through epistatic interactions. In some cases, global epistasis allows evolutionary pathways to be predicted from the fitness of the genetic background alone. In other cases, idiosyncratic epistasis makes evolution less predictable. Here, we show that the evolution of antibiotic resistance is highly repeatable, following a common path across most genetic backgrounds. However, a minority of genetic backgrounds exhibit evolutionary trajectories that significantly deviate from this common path. Rather than being predictable from global epistasis, these deviations are modulated by function-specific epistasis: perturbations to specific cellular functions lead to novel evolutionary trajectories towards resistance. Using tightly controlled robotic evolution experiments, we quantitatively analyzed resistance trajectories for three clinically relevant antibiotics across multiple genetic backgrounds, including hundreds of <i>Escherichia coli</i> gene-deletion strains and several clinical isolates from urinary-tract infections. We show that disrupting distinct sets of cellular functions alters evolutionary trajectories for specific drugs and across different drugs, and we identify genetic changes defining these alternative trajectories. Importantly, this function-specific epistasis often slows down resistance evolution. Some of these effects can also be induced by small-molecule inhibitors of the identified targets, suggesting that function-specific epistasis can be exploited to improve drug treatments.</p>