Florence will remember both accomplishments for a long time.
The Bears overwhelmed the Bruins 49-26 in the Bridgepoint Education Holiday Bowl on Thursday night as Florence threw for two scores and ran for another. Glasco Martin ran for three touchdowns.
Florence completed 10 of 13 passes for 188 yards, giving him 4,309 for the season to break Griffin's school record of 4,293 set in his Heisman Trophy-winning season of 2011.
"For me, I just wanted a chance to play. I just happened to follow a Heisman Trophy winner," Florence said. "I'm not Robert. I'm not 6-3. I don't run a 4.3. You saw that tonight. Man, if I could run a 4.3, it would be nice. So I just had to be me. I tried to manage this offense and play within myself. He's a heck of player, he's done a heck of a job for this program, put us on the map. I'm humbled and honored to hold that record. He deserves it. I never thought that would have happened this year. I just wanted to win games."
Baylor (8-5) won its final four games and five of six.
"That was a question we asked all our players, 'What was going to happen now that Robert's gone?'" coach Art Briles said. "And our guys responded, fought together, believed in each other. They have always sustained and never lost focus."
Lache Seastrunk rushed 16 times for 138 yards and one score for Baylor, which outgained UCLA 494-362. The Bears came in leading the nation in total offense with 578.8 yards per game.
Baylor's defense came up big, too. The Bears sacked Brett Hundley six times, including two by Chris McAllister, and shut down UCLA's career rushing leader Johnathan Franklin. Franklin, who averaged 130.8 yards this season, gained 12 yards on his first carry of the game but was a nonfactor after that, finishing with just 34 yards on 14 carries.
Overall, the Bruins gained only 33 yards on 28 carries. They came in having averaged 202.9 yards rushing.
"They played well up front," UCLA coach Jim Mora said. "When we are at our best is when we can run the football. We couldn't find any room to the football. They played physical."
Hundley was 26-of-50 for 329 yards and three touchdowns to set UCLA's season passing record with 3,740 yards. The old record was 3,470 by Cade McNown in 1998.
UCLA (9-5) lost its final three.
UCLA punted four times and lost the ball on downs before getting a break when Baylor's Jordan Navjar fumbled after a reception when he was hit by Eric Kendricks, with Randal Goforth recovering at the Bears' 21. Two plays later, Joseph Fauria caught a 22-yard pass from Hundley to pull the Bruins to 21-7.
Baylor quickly added two more touchdowns to put it out of reach at 35-7. Martin burst up the middle for his second touchdown of the game, a 26-yarder, and, after UCLA punted yet again, Seastrunk broke free for a 43-yard touchdown run with 1:58 left before halftime.
UCLA then converted two fourth downs, including a fake punt, to move to the Baylor 12 with 7 seconds left. On fourth-and-10, Mora opted to go for a field goal and Ka'imi Fairbairn converted from 30 yards.
Martin added a 1-yard TD run in the third quarter and Florence had a 1-yard scoring run in the fourth.
Martin had 98 yards on 21 carries.
Baylor rushed for 306 yards.
"We knew coming in that we could run the ball well, and the O-line did a heck of a job and made my job easy," Florence said. "It makes throwing a lot easier."
Hundley threw a 24-yard touchdown pass to Shaq Evans early in the fourth quarter and a 34-yarder to Logan Sweet as the game ended.