Insecticide-based vector control is the primary strategy for curtailing dengue transmission. We used a mathematical model of the seasonal population dynamics of the dengue mosquito vector, Aedes aegypti, both to assess the effectiveness of insecticide interventions on reducing adult mosquito abundance and to predict evolutionary trajectories of insecticide resistance. We evaluated interventions that target larvae, adults, or both. We found that larval control and adult control using ultra-low-volume insecticide applications can reduce adult mosquito abundance with effectiveness that depends on the frequency of applications. We also found that year-long continuous larval control and adult control, using either insecticide treatment of surfaces and materials or lethal ovitraps, imposed the greatest selection for resistance. We demonstrated that combined targeting of larvae and adults at the start of the dengue season is optimal. This intervention contrasts with year-long continuous larval control policies adopted in settings in which dengue transmission occurs.