A vehicle includes a hybrid powertrain with a motor/generator electrically coupled to a high-voltage bus to provide propulsion. The vehicle also includes an integrated starter/generator electrically copulated to a low-voltage bus and configured to start the engine. A vehicle power system includes a power converter electrically coupled between the high-voltage bus and the low-voltage bus. During engine start events, operation of the integrated starter/generator is coordinated with operation of the power converter to reduce voltage sag on the low-voltage bus. An increase rate of current supplied to the integrated starter/generator is limited such that a current output of the power converter does not saturate at a maximum current output for a period of time after initiating the engine start event.