To the best of our knowledge, very few efforts have been investigated for separating heterogeneous mixtures methanol/toluene/water with multiazeotropes using extractive dividing-wall column (EDWC). In this work, we propose a systematic approach for the energy-efficient EDWC to achieve less capital cost and operating cost in separating heterogeneous multiazeotropes mixtures, which involves thermodynamic feasible insights via residue curve maps to find separation constraints, global optimization based on a proposed CPOM model, and a dynamic control through Aspen Dynamics simulator to better maintain product purities. An energy-saving EDWC with heat integration (HI-EDWC) flowsheet is then proposed to achieve the minimum total annualized cost (TAC). The computational results show that the TAC of the proposed HI-EDWC is significantly reduced by 15.14% compared with the optimal double-column extractive distillation with an additional decanter. Furthermore, an effective control strategy CS3 with a fixed reboiler duty-to-feed ratio and temperature/(S/F) cascade is proposed to better handle the methanol, toluene, and water product purities than basic control structures CSI and CS2 while feed flow rate and composition disturbances are introduced in the proposed HI-EDWC process.