More than 44,800 fans watched a contest that took nearly four hours to play as Sam Houston rolled up 411 yards total offense against the Big 12 foe.
Baylor quarterback Nick Florence passed for 312 yards and three touchdowns and rushed for 80 more to allow the Bears to rally from a 20-10 halftime deficit.
Quarterback Brian Bell passed for 285 yards and a touchdown. Running back Timothy Flanders rushed for 84 yards and caught three passes for 56 yards. Wide receiver Trey Diller gained 66 yards receiving and 62 yards on punt returns.
Dax Swanson and Bookie Sneed both picked off interceptions. Swanson's marked the 11th of his career, moving him up to third place in SHSU career interceptions. The pick for Sneed his fifth as a Bearkat.
Darnell Taylor led the Bearkat defense with seven stops. Jeremy Jackson and Jesse Beauchamp each was credited with six tackles. Preston Sanders picked up the fourth blocked kick of his career, knocking down a fourth quarter field goal attempt.
"Sam Houston State is a good football team. They're going to beat some people," Baylor head coach Art Briles said. "We're happy to get out of this game with a victory. They were on fire in the first half. We got a couple of big defensive plays in the third quarter and that turned the momentum."
After taking the 10-point halftime lead, Sam Houston stumbled to open the third quarter.
"We really had a bad first five minutes in the second half. It really wasn't even a bad five minutes, it was a bad minute," Sam Houston coach Willie Fritz said.
Baylor opened the scoring with a 33-yard field goal by Aaron Jones after an eight-play, 60-yard game-opening drive.
Sam Houston tied the contest 3-3 on a 31-yard field goal by Miguel Antonio to end a nine-play 39-yard drive with 3:26 left in the period.
After the Bears missed field goal from the 14 yard line, Sam Houston drove 74 yards in 10 plays for a 23-yard field goal by Antonio to give SHSU a 6-3 lead with 14:01 in the second quarter. A 29-yard pass to Timothy Flanders for a first down at the Baylor four was a key play on the drive.
Nick Florence hit Terrance Williams for a 22-yard touchdown to put the Bears back in front 10-6 with 12:52 left in the second period.
Sam Houston bounced back with an eight play, 75-yard drive. Bell hit Trey Diller for 12 yards to the BU 20 then Chance Nelson for 19 yards to the Baylor one before taking the ball in for a touchdown with 10:00 remaining before half to make the score 13-10.
After a Bear punt, the Kats ran their lead up to 20-10 with a 12-play 76-yard drive that ended with a 26-yard Bell to Flanders pass.
Trevor Clemons-Valdez's fumble recovery set up a nine-yard Florence to Lanear Simpson pass to cut the SHSU margin to 20-17 one minute into the third quarter. Florence put the Bears back in front 24-20 with an 18-yard TD pass to Williams with 6:17 remaining in the third.
Sneed 's interception set up a 28-yard field goal by Antonio with 11:17 to play to cut the Baylor lead to 24-23.
Florence broke a 60-yard run and Glasco Martin followed up with a five-yard TD to extend the BU lead to 31-23 with 10:33 to play.
Sam Houston State opens the defense of its 2011 Southland Conference championship next Saturday in Conway as the Bearkats take on last year's league runner-up Central Arkansas in a 3 p.m. contest that will be televised on the Southland TV Network.