This paper investigates the tracking control problem of marine surface vessels (MSVs) in the presence of uncertain dynamics and external disturbances. The facts that actuators are subject to undesirable faults and input saturation are taken into account. Benefiting from the smoothness of the Gaussian error function, a novel saturation function is introduced to replace each nonsmooth actuator saturation nonlinearity. Applying the hand position approach, the original motion dynamics of underactuated MSVs are transformed into a standard integral cascade form so that the vector design method can be used to solve the control problem for underactuated MSVs. By combining the neural network technique and virtual parameter learning algorithm with the vector design method, and introducing an event triggering mechanism, a novel event-triggered indirect neuroadaptive fault-tolerant control scheme is proposed, which has several notable characteristics compared with most existing strategies: 1) it is not only robust and adaptive to uncertain dynamics and external disturbances but is also tolerant to undesirable actuator faults and saturation; 2) it reduces the acting frequency of actuators, thereby decreasing the mechanical wear of the MSV actuators, via the event-triggered control (ETC) technique; 3) it guarantees stable tracking without the a priori knowledge of the dynamics of the MSVs, external disturbances or actuator faults; and 4) it only involves two parameter adaptations - a virtual parameter and a lower bound on the uncertain gains of the actuators - and is thus more affordable to implement. On the basis of the Lyapunov theorem, it is verified that all signals in the tracking control system of the underactuated MSVs are bounded. Finally, the effectiveness of the proposed control scheme is demonstrated by simulations and comparative results.