Three-phase AC–DC rectifiers are fundamental components in modern power electronics systems, yet achieving rapid voltage regulation and precise current tracking under load and grid disturbances remains challenging due to nonlinear dynamics and measurement uncertainties. This paper presents a finite-time control method for three-phase AC–DC rectifiers that achieves millisecond-scale regulation of DC-link voltage and grid currents under varying conditions. The proposed design employs a transformed augmented error-state dynamics model, extending the voltage dynamics to a two-state system to construct an adaptive sliding surface that guarantees fast finite-time convergence. A nonlinear sliding-mode voltage regulator with an online disturbance estimator ensures rapid and robust voltage tracking, while a fast current controller achieves finite-time dq-axis current tracking with minimal chattering. Theoretical results establishes finite-time stability and provides explicit gain selection conditions. Simulation results demonstrate up to 99.40% and 87.5% reductions in voltage and current convergence times, respectively, compared to conventional robust controllers. Laboratory experiments further validate the approach, showing 33.33% lower voltage ripple, 33.33% faster rise time, and 32.43% reduced steady-state error relative to a recent method. These results confirm improvements in transient performance, convergence, and overall system stability, highlighting the method’s practical applicability for high-performance rectifier control.