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 at the lowest engine speeds when the engine-required torque is the highest. This reduces the amount of torque necessary to be supplied from the motor/generator, and further helps to reduce torque disturbances in the driveline. If the motor/generator is producing torque to propel the vehicle at the time the engine start is requested, a launch clutch or one or more transmission clutches can be controlled to provide slip between the motor/generator and the vehicle drive wheels to further reduce torque disturbances in the driveline.