The fundamental question of how the flow velocity of the background plasma can influence the motion of magnetohydrodynamics instabilities and, in the ultimate analysis, their stability is addressed. The growth of resistive-wall-mode instabilities in toroidal confinement devices well represents one example of such a problem. In this Letter, we illustrate a new strategy that allowed, for the first time in a reversed field pinch experiment, a fully controlled rotation of a nonresonant instability by means of a set of active coils and how the new findings compare with numerical modeling.