Blake Szymanski, who was expected to start at quarterback, did not play after missing significant practice time this week because of a bruised shoulder. He got hurt last week in relief of Griffin, who is expected to miss the rest of the season with an isolated tear to the ACL of his right knee.
Florence was 20-of-27 passing for 216 yards and added 60 yards rushing. He gave Baylor (3-1) the lead for good with a 6-yard touchdown run in the second quarter.
"Nick is a confident kid," Bears coach Art Briles said. "He's very poised, very intelligent. He's got a little moxie to him. He did exactly what we thought he'd do."
Jacquise Terry had 109 yards rushing for Kent State (2-3), including a 61-yard scoring run in the third.
Baylor's Kendall Wright caught nine passes for 125 yards, and Jarred Salubi rushed for 64 yards and a touchdown in support of the freshman Florence.
Griffin, who passed for 2,091 yards and 15 touchdowns as a freshman in 2008, spent the first half on the sidelines wearing a headset. During pregame warmups, Griffin gingerly walked around while encouraging some of his teammates and even lobbed a couple of soft tosses while playing catch in the end zone.
The star quarterback wasn't the only offensive starter in street clothes for Baylor. Starting running back Jay Finley missed his second straight game with an ankle injury.
Even with most of their starting backfield missing, the Bears had 374 yards of offense.
Florence capped an 89-yard drive with a 6-yard run that finished by diving into the end zone. This gave the Bears a 14-7 lead with 13:02 left in the first half.
The score came three plays after he hit Wright on a screen pass, which the speedy receiver turned into a 44-yard gain.
Salubi's 45-yard touchdown run gave the Bears a 21-7 halftime lead. Then Florence showed off his athletic ability on the opening drive of the second half.
Florence scampered for gains of 14 and 10 before his 29-yard scoring run gave the Bears a 21-point lead.
Terry, who had his second straight 100-yard game, brought Kent State within 28-13 with his touchdown.
The Golden Flashes drove deep into Bears territory three times after that but only scored a safety. Freddy Cortez missed a field goal and Kent State was stopped twice on fourth-down attempts inside the 10, including once on a fake field goal.
Kent State has lost all three of its games this season to schools from BCS conferences.
