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.
The Bruins were never in this one. Baylor raced to a 21-0 lead by early in the second quarter on Martin's 4-yard run and Florence's TD passes of 8 yards to Antwan Goodley and 55 yards to Tevin Reese.
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.