Mike Gillislee rushed for 79 yards and a score for the Gators (2-0), who were coming off last weekend's 41-3 drubbing of Florida Atlantic. John Brantley completed 12-of-19 passes for 195 yards in the win.
Bryan Ellis passed for 141 yards for the Blazers (0-1), who gained just 212 total yards.
"I would like to congratulate the University of Florida for winning the football game pretty handily. Obviously disappointed in the outcome," said UAB head coach Neil Callaway.
The Gators controlled the game from the outset, scoring 13 points in the first quarter. Caleb Sturgis hit field goals of 24 and 35 yards on Florida's opening two possessions, and after UAB went three-and-out, the Gators found the end zone.
Hunter Joyer's three-yard run capped an eight-play, 73-yard march with two minutes left in the opening quarter.
Sturgis' 28-yarder with 4:10 left in the half expanded Florida's lead, which grew again on the following UAB drive, when a botched punt led to a Gators safety.
Florida's offense then needed only four plays to reach the end zone. Starting at the Blazers' 37, the Gators quickly went downfield. Brantley completed an 18-yard pass to Andre Debose before Rainey's nine-yard run, which set up a five-yard TD rush by Trey Burton.
The score came with 1:09 left on the clock and had Florida leading 25-0 at the break.
Rainey's 19-yard TD run early in the third quarter and Gillislee's 13-yard dash with 6:25 left completed the scoring.
"I'm just doing my job, trying to score touchdowns for the team. I have to give a lot of credit to the offensive line and receivers," Rainey said.
Florida beat UAB, 51-3, in 2002, the only previous meeting between the programs...The Blazers had 11 first downs and held the ball for 23:31...Florida opens SEC play next Saturday, when it hosts Tennessee.