A control device for a drivetrain of a vehicle, includes a drive engine, a starting element, and a coupling element. The coupling element brakes a secondary side when the control device receives an input signal indicating a switching off of the drive engine. The starting element includes a mass damper torsional damper arrangement with at least one damper mass. The starting element is coupled with the drive engine by a primary side and with the mass damper torsional damper arrangement by a secondary side so as to be fixed with respect to relative rotation, and the coupling element is constructed to brake the secondary side by coupling with the primary side of the starting element and/or by coupling with a reference component that stationary when the vehicle is stationary. This makes it possible to find a better compromise between comfort, responsiveness, economical, and ecological aspects of the drivetrain.