Direct-acting antiviral agents (DAAs) provide efficacious therapeutic treatments for chronic Hepatitis C virus (HCV) infection. However, emergence of drug resistance mutations (DRMs) can greatly affect treatment outcomes and impede virological cure. While multiple DRMs have been observed for all currently used DAAs, the evolutionary determinants of such mutations are not currently well understood. Here, by considering DAAs targeting the nonstructural 3 (NS3) protein of HCV, we present results suggesting that epistasis plays an important role in the evolution of DRMs. Using a sequence-based fitness landscape model that we validate using experimental data, we identify specific DRMs that are associated with strong epistatic interactions, and these are found to be enriched in multiple NS3-specific DAAs. We further demonstrate, using evolutionary modelling, that the identified DRMs involve compensatory mutational interactions that facilitate relatively easy escape from drug-induced selection pressures. Our results indicate that accounting for epistasis is important for designing future HCV NS3-targeting DAAs.