A new sensor-based homing integrated guidance and control law is presented to drive an underactuated autonomous underwater vehicle (AUV) toward a fixed target, in 3-D, using the information provided by an ultra-short baseline (USBL) positioning system. The guidance and control law is first derived at a kinematic level, expressed on the space of the time differences of arrival (TDOAs), as directly measured by the USBL sensor, and assuming the plane wave approximation. Afterwards, the control law is extended for the dynamics of an underactuated AUV resorting to backstepping techniques. The proposed Lyapunov-based control law yields almost global asymptotic stability (AGAS) in the absence of external disturbances and is further extended, keeping the same properties, to the case where known ocean currents affect the motion of the vehicle. Simulations are presented and discussed that illustrate the performance and behavior of the overall closed-loop system in the presence of realistic sensor measurements and actuator saturation.