A yaw angle, different from zero, introduces highly nonlinear couplings in the rotational and translational quadrotor dynamics, implying undesirable motions. This argument has motivated that the position control problem of quadrotors is studied generally regulating yaw at zero. However, zeroing yaw limits the maneuverability of underactuated quadrotors because yaw is one of the four actuated motions. In this paper, the simultaneous tracking of position and time-varying heading is proposed, based on an integral sliding mode control with a quaternion-based sliding surface. An exponential tracking with chattering-free is obtained without requiring any knowledge of the dynamic model or its parameters for implementation. Since a linear invariant orientation error manifold is enforced for all time, a time-varying gain is introduced for a well-posed finite time convergence, which is useful not only to realize the virtual position control scheme, due to underactuation, but also to guarantee a desired contact in a given point at a given desired contact time for the yaw motion. Illustrative applications are explored in a simulation study which shows the viability and versatility of position–yaw tracking in the surveillance of a field-of-view (FoV) target, aerial screw driver, and aerial grasping.