Davies tapped in after a shot by new signing Wes Thomas was tipped onto the bar by goalkeeper Chris Maxwell.
The away side had earlier taken the lead when Jamille Matt rose highest to head home Jimmy Ryan's long ball.
James Hanson headed Bradford level eight minutes later and Billy Knott fired over following Tony McMahon's free-kick but Davies' goal won it.
The result moves Bradford up to 10th, just three points from the play-off places, while Fleetwood occupy the relegation zone in 21st place.
Substitute Steven Davies scored in added time to give Bradford victory over League One strugglers Fleetwood.