Baylor (7-5, 4-5 Big 12) has won at least seven games in three straight seasons - the first time the Bears have done that since 1949-51.
Seastrunk's long scoring run gave Baylor a 41-27 lead with 5:11 left in the game.
The sophomore burst through the middle and slowed down about 25 yards shy of the end zone. Seastrunk stumbled into the end zone and was down on the turf before limping off with an apparent right leg injury.
Baylor recovered the ensuing onside kick and ran out the clock to secure its third straight victory. The Bears had lost six in a row to the Cowboys by an average of 31.7 points.
Bears linebacker Eddie Lackey returned an interception for a touchdown in the first quarter to help Baylor jump out to a 21-point lead in the first half.
Florence threw a 75-yard touchdown pass to Tevin Reese and the senior quarterback also rushed for 71 yards and a score in the final home game of his career.
Florence has thrown for 4,121 yards this season and is 172 yards shy of breaking the school's single-season passing mark, which Robert Griffin III set last season.
After sputtering offensively most of the second half, Oklahoma State drove 88 yards to make it 34-27 on Walsh's 4-yard touchdown run with 5:30 left in the game.
On the next play from scrimmage, Seastrunk broke loose for his 76-yard touchdown. As soon as he crossed the goal line, the Baylor crowd began chanting his name.
Seastrunk stayed on the sideline for the final minutes, but he didn't return to the game.
The Bears took the lead for good early on Lackey's second interception return for a touchdown in two games.
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.
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