A vehicle propulsion system includes an engine and a first electric machine each configured to selectively provide torque to propel the vehicle. The propulsion system also includes a second electric machine coupled to the engine and configured to start the engine from an inactive state. A high-voltage battery powers both of the first electric machine and the second electric machine over a high-voltage bus. The vehicle further includes a controller programmed to issue a command to start the engine using the second electric machine in response to a threshold acceleration demand following a period of reduced acceleration demand.