Davies brought down Albion's Jacques Maghoma ten minutes into the second half and referee Gary Sutton was quick to point to the spot, and even quicker to produce his card.
Maghoma converted from the penalty spot to hand Gary Rowett's men a slender advantage -
which was doubled by Billy Kee with a quarter of an hour remaining.
Some casual defending from Fleetwood gifted the former Torquay striker space on the edge of the box and his 19-yard effort was placed to perfection, dropping off the angle past stand-in stopper David Lucas.
Fleetwood threw Jamille Matt into the action in the hope of finding a way back. And they came close when David Ball let rip from the left flank and Stuart Tomlinson almost spilled the ball into the path of Jean Michel Fontaine.
But Burton sealed victory with three minutes remaining when substitute Calvin Zola picked out the run of Maghoma and the tricky winger slid the ball low past Lucas.
The visitors added a fourth in injury time when Maghoma found space down the left and chose to pass rather than shoot, leaving Zola with a tap in.