A hybrid electric powertrain includes an electric machine delivering torque to an engine in an engine start event having initial cranking and transition phases. In response to a request for an engine start event, a controller commands delivery of the motor torque to the crankshaft. In the initial cranking phase the controller regulates crankshaft acceleration from zero speed up to a target cranking speed in a closed-loop manner via a predetermined fixed profile. In the transition phase, the crankshaft accelerates from the target cranking speed to a target idle speed using a feed-forward torque value blended, using a calibration table, from a predetermined engine drag torque to a reported engine torque. In the transition phase the controller periodically adjusts a speed trajectory of the crankshaft, with the magnitude and frequency of adjustment based on combustion of the engine and calibration of the feed-forward torque.