A hybrid powertrain is provided that provides engine starting from an electric-only mode with a reduced torque load on the motor/generator. The powertrain includes an engine and a motor/generator, which may be a single motor/generator in a strong or full hybrid, but is not limited to such. The motor provides propulsion torque in an electric-only operating mode, and is configured to apply torque to a transmission input member. A first clutch is selectively engagable to connect the engine output member for common rotation with the transmission input member. An engine starting mechanism is provided that multiplies motor torque used to start the engine so that less is diverted from propelling the vehicle, enabling a smaller motor/generator to be used. A method of controlling such a powertrain is also provided.