This paper contributes to an anti-windup control scheme for path-following of underactuated autonomous underwater vehicles (AUVs) subject to constrained inputs. First, a disturbance observer is employed to estimate the model uncertainties and external disturbances on the nominal vehicle model, which are referred to as mismatched lumped disturbances. On the basis of that, a three-time scale singular perturbation control law is proposed, taking advantage of the time scale separation caused by the different rates of various variables. Furthermore, a novel disturbance observer-based anti-windup modification is developed to handle possible input saturation. And stability for the singularly perturbed system subject to actuator saturation is also established, using a method called "manifold reconfiguration" in a geometric view. This results in a relatively simple constrained controller and reduces implementation complexity. Finally, simulation and experimental results are presented to substantiate the effectiveness of the proposed method for path-following of underactuated AUVs exposed to unknown disturbances and input constraints.