In this study, a robust finite-time (FnT) sliding mode attitude and position control is proposed for the precise tracking of an underactuated quadrotor unmanned aerial vehicle (QUAV) subjected to multiple sources of uncertainties, i.e., unmodeled dynamics, external perturbations, and parameter uncertainties. The proposed flight control system is based on the nonsingular integral terminal sliding control (NITSMC) to ensure rapid tracking of the targeted 3D trajectories while reducing the steady state-errors. The performances of the control system are enhanced through the introduction of a disturbance observer (DO) that estimates unknown external disturbances and enhances the system’s robustness. Stability analysis and FnT convergence are verified using the Lyapunov stability analysis. Finally, comparative simulations under different flight conditions are performed to assess the accuracy and robustness of the suggested controller. The obtained results highlight the improved performance of the suggested approach in terms of accuracy, rapidity, and robustness against wind disturbances.