This paper addresses the problem of trajectory tracking control of an underactuated surface vessel moving in a two-dimensional space in the presence of unknown disturbances. In a preliminary stage, a couple of nonlinear observers is derived to obtain an estimate of the perturbations, which are assumed to originate from unmodeled time-varying dynamics and/or exogenous disturbances. Secondly, we resort to the Lyapunov-based backstepping technique to design two stabilizing control laws, governing the thrust force and torque actuations, that are proved to render the overall control system error globally uniformly bounded. Each control law yields an actuator signal which is implicitly bounded with respect to the position error, and the resulting estimation and tracking errors can be made arbitrarily small by tweaking the control parameters. A set of realistic simulations results is presented to validate our strategy. Experimental trials using an autonomous surface vehicle are also showcased to further demonstrate the efficacy and robustness of the proposed controller.