Hot dry rock (HDR) geothermal energy is an abundant and sustainable energy resource. Among existing extraction methods, Enhanced Geothermal Systems (EGS) represent the most practically feasible solution, yet they still face challenges such as rapid thermal breakthrough, short operational lifespan, and swift thermal decay. To overcome these limitations, this study proposes an Electric-field-enhanced Geothermal System (EEGS), which actively regulates fluid and heat transport through electroosmotic flow. A novel thermal-hydraulic-electrical coupling model was developed, comprehensively considering Darcy flow, electroosmotic flow, thermal convection, conduction, and Joule heating effects, and was validated against analytical solutions. Based on the temperature evolution and its derivative at the production well, four stages of thermal response were identified: a fracture-dominated accelerated heat transfer stage, a fracture-matrix exchange-dominated deceleration stage, a matrix-dominated accelerated heat transfer stage, and a steady-state conduction stage. Applying a 200 V DC electric field opposite to the natural flow direction delayed the thermal breakthrough time from 31.7 years to 59.2 years (an 86.7% delay) and increased the average outlet temperature at 80 years from 379.97 K to 478.53 K (a 25.95% increase). The results indicate that electroosmotic flow plays a dominant role in transport regulation, while the influence of Joule heating is negligible. Parameter studies revealed that increasing the injection pressure from 79 MPa to 88 MPa advanced the thermal breakthrough time from 66.4 years to 24.5 years (a 63.2% reduction); whereas decreasing the injection temperature from 313.15 K to 288.15 K advanced the thermal breakthrough from 39.1 years to 28.9 years (a 26.1% reduction). An economic assessment demonstrates that EEGS has significant economic viability, with an Energy Return on Investment (EROI) greater than 1, particularly when integrated with curtailed wind or solar power. EEGS offers a non-thermal mechanism for improving geothermal energy efficiency and lifespan, and can be flexibly combined with intermittent renewable energy sources (such as wind or solar) to create hybrid systems with higher thermal stability and more sustainable energy output.