The Cod Army took the lead through Matty Blair with 19 minutes to go yet Bennett's three-minute double salvo shortly afterwards turned the game on its head.
The Grecians, with five men at the back, set out to limit their hosts in the first 45 minutes.
But Fleetwood still created chances, Steven Schumacher with a long-range drive tipped over the bar by Artur Krysiak. Nathan Pond headed towards goal from the resulting corner but his effort was also kept at bay by the visiting stopper.
After the interval Graham Alexander's side upped the pressure, Jeff Hughes with a shot saved and Antoni Sarcevic almost sending David Ball through, the striker getting the ball caught under his feet.
The breakthrough came courtesy of substitute Blair, who found space at the back post to slam home Conor McLaughlin's deep cross.
But the visitors were level within five minutes, Alan Gow slipping in Bennett whose neat finish beat Scott Davies in the Fleetwood goal.
And the tables were turned when Gow slid past McLaughlin and his pinpoint cross was perfect for Bennett to fire the Grecians ahead.
He nearly had a hat-trick following a mix up at the back for the Cod Army but Davies slid in to clear.