A widespread experimental realization of quantized anomalous transport in the intrinsic magnetic topological insulator MnBi₂Te₄ is hindered by its elusive surface magnetic gap. Uncovering the origin of the gapless states is essential for accessing its topological properties. Here we show that surface defects lower the electrostatic potential, drive topological surface states into subsurface layers, suppress exchange interactions, thereby closing the gap. Tuning the surface electrostatic potential via external electric fields or interfacial fields in van der Waals heterostructures restores the expected gap and enables control of its topology. This is confirmed by model calculations and validated in defective MnBi₂Te₄ films interfaced with polar insulators, explaining the enhanced quantum anomalous Hall effect under AlOₓ capping observed in recent experiments. Our theory identifies electrostatically driven surface-state delocalization as a competitive origin of gap suppression and proposes displacement-field engineering for robust quantized transport.