A method for stabilizing constrained mechanical systems that is based on the so-called constraint stabilization technique is proposed. It extends the approach that was earlier employed for numerical integration of equations governing motion of passive constrained mechanical systems to the case of controlled systems. In the framework of the suggested approach, control goals are treated as additional constraints, and the controls themselves, as constraint reactions. The application of the method to the problem of stabilizing a wheel rolling along a curvilinear profile is considered.