Professional drivers in drifting competitions demonstrate accurate control over a car's position and sideslip while operating in an unstable region of state-space. Could similar approaches help autonomous cars contend with excursions past the stable handling limits, thereby improving overall safety outcomes? As a first step towards answering that question, this paper presents a novel controller framework for automated drifting along a path. The controller is derived for the general case, without reference to a nearby equilibrium point. This leads to the physically insightful result that one can use the rotation rate of the vehicle's velocity vector to track the path, while simultaneously using the yaw acceleration to stabilize sideslip. Nonlinear model inversion, in concert with low-level wheelspeed control, is then used to achieve these required state derivatives over a broad range of conditions. Experiments on MARTY, a modified 1981 DMC DeLorean, demonstrate excellent tracking of a trajectory with varying curvature, speed, and sideslip. Comparisons to a test run without wheelspeed control highlight the importance of accounting for the rear saturated-tire wheelspeed dynamics.