Redshirt freshman quarterback Feleipe Franks was 10-of-14 passing for 185 yards in place of Del Rio and guided the Gators (3-1, 3-0 SEC) on three second-half touchdown drives. Franks entered when Del Rio injured his left shoulder and helped the Gators defeat Vanderbilt for the 26th time in the past 27 meetings.
Perine, a sophomore, is the first Florida player to score three touchdowns in a single game since quarterback Jeff Driskel in 2012 and the first running back to do so since DeShawn Wynn in 2005.
Commodores junior quarterback Kyle Shurmur threw for 264 yards and three touchdowns but completed just 18 of 40 attempts. The loss was the second in a row for Vanderbilt (3-2, 0-2), which was trounced 59-0 by Alabama one week earlier.
Shurmur attempted to rally the Commodores from a two-touchdown deficit and threw a 7-yard touchdown pass to senior tight end Nathan Marcus to cap a 14-play, 77-yard drive and pull the Commodores within 31-24 with 3:14 to play.
Florida went for it on fourth-and-1 on its next drive and Davis exploded through the right side of the line for a decisive 39-yard scoring run with 1:42 remaining.
Earlier, Davis put the Gators ahead for good at 24-17 with a 1-yard scoring run with 6:56 left in the third quarter. Perine tacked on a 1-yard run 42 seconds into the fourth quarter to make it a 14-point margin.
Del Rio was knocked out of the game when he took a solid hit with just under five minutes left in the second quarter. Vanderbilt junior defensive end Dare Odeyingbo applied pressure and hit Del Rio just after he unleashed a pass and the Florida junior landed hard on his surgically repaired non-throwing shoulder.
Franks entered when the Gators next had the ball with 3:23 left as Del Rio headed to the locker room.
Franks started Florida's first three games but lost his job when Del Rio rallied the Gators to a victory over Kentucky last Saturday.
Perine got Florida on the board with a 1-yard scoring run with 6:12 left in the opening period before the Commodores tied it nearly four minutes later when Shurmur tossed a 13-yard touchdown pass to sophomore receiver Kalija Lipscomb.
Perine's 13-yard scoring dash gave the Gators a 14-7 advantage with 10:03 remaining in the first half. Shurmur connected with senior receiver Caleb Scott on a 12-yard tying pass with 6:51 remaining before the teams traded field goals in the final minute for the 17-17 halftime score.
NOTES: Florida was again without nine suspended players who have been charged with a collective 62 felony counts of fraud in a credit-card scandal. The list includes standout junior WR Antonio Callaway and junior RB Jordan Scarlett. ... Vanderbilt senior RB Ralph Webb was limited to 29 yards on 11 carries. He has just 198 yards this season after setting a school record with 1,283 last season. ... Florida QB Luke Del Rio went 5-1 as a starter last season before suffering knee and shoulder injuries that required offseason surgeries. ... The Commodores' lone win over the Gators since 1988 occurred in a 2013 visit to Gainesville. ... Florida running backs had gone nine consecutive games without a rushing touchdown until breaking out with five versus Vanderbilt.