The junior linebacker picked off a short pass in the flat and ran untouched for a 26-yard touchdown that gave Baylor a 10-3 lead with 7:58 remaining in the first quarter.
The Bears scored on their next two possessions to build a 24-3 lead. Glasco Martin powered in for a 2-yard touchdown run to cap a 16-play, 98-yard drive.
Florence then found Reese for a 75-yard touchdown pass. Reese caught the ball at the 40 and raced past three Oklahoma State defenders into the end zone.
The Cowboys got within 24-17 with consecutive touchdowns. Walsh had a 1-yard run and Chelf threw a 15-yard scoring pass to Stewart.
Chelf was 30 of 51 for 333 yards with two touchdowns and two interceptions.
Florence's 3-yard touchdown run made it 31-17 with 3:33 left in the first half.
Oklahoma State tight end Blake Jackson dropped two potential touchdown passes in the game. He had one on the Cowboys' first drive of the game and again early in the third quarter.
The Cowboys were able to kick field goals after the drops, including Quinn Sharp's 43-yarder in the third quarter that made it 31-20.