A vehicle includes a motor/generator, a disconnect clutch disposed between the engine and the motor/generator, and a transmission disposed between the motor/generator and the vehicle drive wheels. The transmission includes an input clutch which is selectively engagable for facilitating torque transfer between the motor/generator and the vehicle drive wheels. When an engine start is requested, the motor/generator is operated, and a start mode for the engine is determined based on a number of vehicle parameters. The transmission input clutch is partially disengaged to at least partially isolate the vehicle drive wheels from engine torque disturbances when the engine is started. The disconnect clutch is engaged, and the engine is fueled, thereby facilitating torque production by the engine.