Controlling collective electronic phases in low-dimensional materials is a central challenge for developing technologies based on charge-density waves. Here, we report that perpendicular electric and magnetic fields can be used to tune charge-density-wave transport in the quasi-two-dimensional material 1T-TaS2. Using h-BN-encapsulated thin-film heterostructures with both top-gate and bottom-gate configurations, we find that electrical gating produces a non-monotonic shift in the depinning threshold, a behavior distinct from that of quasi-one-dimensional charge-density-wave systems. We further show that a perpendicular magnetic field increases the threshold voltage for domain depinning and can drive the nearly commensurate-to-incommensurate charge-density-wave phase transition, demonstrating magnetic control over a two-dimensional electron-lattice condensate. The obtained results shed light on mechanisms governing charge-density-wave domain dynamics and reveal combined electrical and magnetic-field control as a strategy for engineering low-power-dissipation devices and electronics for extreme environments.