Fox began the day three shots adrift and when he dropped three shots at the third he looked out of contention.
But he regained ground with a couple of birdies and then came home in 31 to finish on 18 under and edge out England's home favourites Tyrrell Hatton and Aaron Rai.
Spain's world number three Jon Rahm finished with a 68 for a 16 under total, one ahead of Ryder Cup team mate Viktor Hovland and two clear of another Ryder Cup player Tommy Fleetwood.
World number two Rory McIlroy caught fire in his fourth round with a 65 to finish at 13 under.
Fox had never managed a top-10 finish at the Wentworth event but arrived in good form after a finishing tied third at last week's Horizon Irish Open.
He is the first New Zealander to win the tournament.
