Pervaporation is typically considered an energy-efficient technology for the separation of azeotropic mixtures. However, the vaporization of the permeate leads to a temperature drop in the residual stream, and a supply of external energy is required to maintain a constant residual stream temperature in traditional pervaporation processes, which lowers their energy efficiency. Therefore, in this study, a heat-integrated pervaporation−distillation hybrid system was designed and investigated for the separation of an azeotropic MeAc−MeOH mixture using a low-temperature residual stream to cool the top vapor of the column. The temperature drop in the residual stream during pervaporation was studied using simulations and experiments. Pervaporation−distillation hybrid processes with and without heat integration were simulated and compared with special distillation under various operating parameters; their energy efficiencies were also compared. The results indicated that pervaporation−distillation with heat integration can lower the energy consumption by 24% compared to that via pressurized distillation with heat integration. Additionally, the energy efficiency increased by 31.7% compared to that by pressurized distillation with heat integration at a MeAc feed concentration of 50 wt %. The system proposed in this study is simple and practical for the energy-efficient design of pervaporation setups in industrial settings.