Cancer treatment has greatly benefited from the introduction of both new agents (i.e. targeted therapy and check point inhibitors) and new strategies for conventional therapies such as chemotherapy and hormonal therapy. Most cancer types now have at least one effective treatment agent, and many tumors, such as breast and prostate cancer, have multiple available treatment options. However, even the most effective therapy is usually defeated as cancer cells deploy a wide range of molecular strategies to overcome therapy leading to disease progression. Here we propose that, while molecular dynamics govern response and resistance to therapy, evolutionary dynamics determine survival and proliferation of treatment-resistant cells. We hypothesize that understanding these evolutionary interactions may identify strategies to delay or prevent proliferation of resistant population thus prolong time to recurrence. To simulate these interactions, we use an off-lattice, agent-based, framework to model competition between sensitive and resistant populations during therapy in a spatially competitive environment. Our model applies a classic evolutionary trade-off between fecundity (cellular proliferation) and survivorship (drug sensitivity) to the tumor populations. Thus, in the resource-limited tumor microenvironment, the cost of increased resource investment in a resistant phenotype necessarily results in slower proliferation while a phenotype invested in fast proliferation is less likely to survive in drug. Model simulations demonstrate that, in the absence of therapy, cells with slower growth but higher survivorship may become confined in the interior of the tumor during growth phases, which provides a spatial sanctuary during initial drug administration. Over time, therapy eliminates the treatment-sensitive population allowing the resistant cells to proliferate unopposed. We simulate the application of an anti-proliferative drug on varying ratios of mixed sensitive and resistant cells using two general treatment strategies: a continuous schedule of maximum tolerated dose or an evolution-informed schedule that incorporates dose-modulation and treatment vacations to sustain control of the tumor through competition between sensitive and resistant cell populations. We find tumors consisting only of sensitive cells can cured with continuous treatment, but the presence of any significant population of resistant cells will lead to eventual recurrence. We identify two treatment strategies that control heterogeneous tumors: one emphasizes continuous dose modulation, and the other relies on treatment vacations. Both strategies control tumors over a wide range of resistant/sensitive population ratios but the average dose given is significantly lower with dose modulation. Cell migration and phenotypic drift limit the time to recurrence advantage of these strategies but some efficacy can be retained through a more vacation-oriented schedule.