Town had the chance to grab an early lead when Ryan Crowther headed over from six yards. And they were made to pay at the other end just 12 minutes in.
Chris Hussey swung in a teasing ball from the left, Adam McGurk's spectacular overhead kick attempt distracted the Town defence just long enough for Rene Howe to sneak in at the back post and fire the Brewers ahead.
Burton were making the better of the sodden conditions at Highbury and doubled their advantage when Hussey's low corner skidded across the Fleetwood box, McGurk applying the final touch.
It became three-nil before the break, some poor defending from Fleetwood allowing Howe the space to flick the ball on, Hussey firing in off a post.
Fleetwood looked sunk, but two goals in eight second-half minutes gave them hope.
Substitute Gareth Evans set up the first, driving down the left before his pass picked out a determined Jeff Hughes, who kept his feet and his head to fire through a crowded box.
When Antoni Sarcevic bulldozed his way to the byline to set up Jamille Matt for his first of the campaign an unlikely comeback appeared on the cards.
But Fleetwood could not find a way through, Burton hanging on to take the honours as Junior Brown's last-ditch free-kick flew wide.