A unified control device for engine and automatic transmission of an automotive vehicles serves to alleviate a racing select shock which occurs upon engagement of a driving clutch in the transmission when selecting a running range of the transmission to start the vehicle with an accelerator pedal depressed. The control device achieves a reduction control during changeover of the transmission into a running range from a racing state, to reduce at least one parameter representing the output power to be transmitted from the engine to driving wheels via the transmission, such as engine speed, engine output and/or transfer torque capacity of the clutch, etc. The reduction control is stopped as soon as the completion of engagement of the driving clutch has been detected, to allow the vehicle to be started without engine stalling.