Control systems education often faces a dichotomy between costly physical laboratories and accessible but numerically inaccurate simulation platforms, such as web-based simulators. Existing web-solutions typically rely on low-order integration methods, failing to capture realistic non-linear behaviors crucial for industrial applications. This study addresses these limitations by developing a high-fidelity, client-side Virtual Laboratory for DC Motor control. The novelty of this work lies in the integration of the Runge-Kutta 4th Order (RK4) algorithm within a lightweight HTML5/JavaScript architecture, eliminating server-side latency while ensuring superior numerical precision over standard Euler-based applets. Furthermore, the system implements a realistic discrete PID controller with a Conditional Integration (Clamping) Anti-Windup strategy, enabling precise analysis of actuator saturation effects. Validation benchmarks against standard numerical computing software like GNU Octave demonstrate rigorous accuracy. The proposed system achieves a steady-state relative error of less than 0.001% and shows negligible deviation in transient response metrics (rise time, settling time, and overshoot). Additionally, the virtual lab maintains identical closed-loop pole locations up to four decimal places. By integrating real-time Bode Plot and Root Locus analysis, this platform provides a robust, open-access tool that effectively bridges the gap between theoretical design and practical non-linear implementation challenges.