In this paper, we show how evolutionary game theory can be embedded into a traditional optimal control framework in order to predict strategies for time-dependent drug dosages in the context of a growing pathogen population that exhibits the capacity to evolve in direct response to the level of applied drug. To illustrate our method for integrating evolutionary games with optimal control systems, we consider a simplified model that describes a generic trade-off between viral replication rate and drug resistance. The technique that we outline, however, is readily extendable to more complicated models that account, in more detail, for the specific biology of a particular pathogen of interest.