A vehicle control method includes, by a controller, while an engine is auto-stopped and an electric parking brake is engaged, auto-starting the engine without releasing the electric parking brake responsive to application of an accelerator pedal less than a predefined amount, and auto-starting the engine and releasing the electric parking brake responsive to application of the accelerator pedal greater than the predefined amount. The method also includes comprising auto-stopping the engine and engaging the electric parking brake responsive to vehicle speed being less than a predefined threshold speed.