Failure to clear antigens causes CD8+ T cells to become increasingly hypo-functional, a state known as exhaustion. We combined manually extracted information from published literature with gene expression data from diverse model systems to infer a set of molecular regulatory interactions that underpin exhaustion. Topological analysis and simulation modeling of the network suggests CD8+ T cells undergo 2 major transitions in state following stimulation. The time cells spend in the earlier pro-memory/proliferative (PP) state is a fixed and inherent property of the network structure. Transition to the second state is necessary for exhaustion. Combining insights from network topology analysis and simulation modeling, we predict the extent to which each node in our network drives cells towards an exhausted state. We demonstrate the utility of our approach by experimentally testing the prediction that drug-induced interference with EZH2 function increases the proportion of pro-memory/proliferative cells in the early days post-activation.