The unpinning of a spiral wave from an anatomic obstacle by the application of a single stimulus near the core of the rotating wave was studied experimentally in a cell culture of cardiomyocyte monolayers as well as by computer simulations. It is shown that, with suitable positioning and timing, a single stimulus is sufficient for the successful unpinning of a pinned spiral wave. Successful unpinning is achieved when two conditions are fulfilled: (1) The stimulus is delivered in the vulnerable window of the rotating wave, and (2) the stimulus is delivered in a spatial zone in proximity to the obstacle, where the shape of the zone is defined by the phase of the anchored spiral wave. Two different scenarios for successful unpinning are discussed, which are distinguished by the distance to the stimuli applied to the obstacle.