Electrification of distillation processes through discretely heat integrated distillation columns (D-HIDiC) is an effective approach to enhance energy efficiency and lower carbon emissions. For separating systems with high temperature lift, multi-stage compression and inter-stage cooling are necessary to link the high-pressure rectifier and low-pressure stripper. Traditionally, heat recovery employs pumparound loops, but this study introduces liquid injection as a more efficient and innovative alternative. Simulation results using methanol/water separation indicate that liquid injection reduces both reboiler duty and compression power, achieving up to 50% primary energy savings compared with conventional distillation columns. Unlike continuous heat exchange in conventional HIDiC (C-HIDiC), D-HIDiC simplifies heat integration, avoiding complex hardware and energy penalties. Comparative analysis across multiple configurations, including SuperHIDiC, confirms the potential of D-HIDiC with liquid injection to fully electrify distillation, eliminate steam utility, and significantly support sustainable industrial operations.