A vehicle includes a motor/generator, a starter motor, a disconnect clutch disposed between the engine and the motor/generator, and at least one clutch disposed between the motor/generator and the vehicle drive wheels. When an engine start is requested, various parameters are controlled to ensure a smooth engine start wherein driveline torque disturbances are minimized. The starter motor is used to crank the engine upon an engine start request, thereby eliminating the need to transfer torque from the motor/generator to the engine. This helps to further reduce torque disturbances in the driveline when the engine is started.