Fleetwood gave the Grecians an early lead with a superb 25-yard strike. Dagenham pulled level in the 36th minute when a mistake by Paul Jones allowed Ben Strevens to equalise.
Three minutes after the restart Fleetwood, making only his second start for the Grecians, produced another piece of individual magic when he fired an unstoppable volley past Tony Roberts.
Strevens had the first shot of the game for the visitors with a volley which flew over the bar.
The game burst into life in the 16th minute. There seemed little when danger when Fleetwood controlled the ball 30 yards from goal, but he twisted and turned and curled a majestic strike from 25 yards into the top corner.
Exeter allowed the Daggers back into the game and Jamie Gain forced Jones to save well with a fine strike from the edge of the box.
Matt Richie then picked out Sam Saunders who fired the ball into the arms of Jones from 15 yards as Dagenham pressed forward.
They equalised when Jones collided with his centre-back Troy Archibald-Henville while trying to collect Richie's long ball and Strevens slotting the ball into an empty net from a tight angle.
Exeter were ahead again three minutes after the restart. Matt Gill's throw was chested down by Fleetwood with his back to goal and he turned and struck at unstoppable volley into the top corner from the edge of the box.
Fleetwood might have had a hat-trick when he was found by Adam Stansfield, but his close-range strike was well saved by Roberts.
Bertrand Cozic then headed into the arms of the goalkeeper from Gill's cross, as the Grecians ended the game strongly and were good value for another crucial three points.