He completed 26 of 42 passes for 367 yards, 137 of which went to Terrance Williams on 11 receptions.
The Bears (4-4, 1-4 Big 12) took a 20-14 lead into halftime, when lightning struck near the stadium and caused a 30-minute delay.
Baylor seemed determined to pick up its first conference victory, though, and outscored the Jayhawks 14-0 in the third quarter to put the game out of reach. Bryce Petty scored from 1 yard out on his only carry to make it 27-14 and Florence followed that up with his touchdown run.
James Sims rushed 21 times for 127 yards and a touchdown for Kansas, which dropped to 1-8 overall and 0-6 in conference play. The Jayhawks travel to Texas Tech next week.