A vehicle includes an engine and an electric machine coupled to a gearbox. A controller is programmed to predict, at an onset of a shift, a supplemental torque profile to fill a torque hole expected during the shift and an available electric machine torque during the shift. The controller is further programmed to, in response to the supplemental torque profile exceeding the available electric machine torque during the shift, operate the engine from the onset to achieve a torque reserve in anticipation of increasing the engine torque.