Griffin threw for 479 yards and four touchdowns, including a 34-yarder to Terrance Williams with 8 seconds left and 25th-ranked Baylor beat the Sooners for the first time, 45-38 on Saturday night.
The Sooners (8-2, 5-2 Big 12) had overcome a two-touchdown deficit to tie the game on Blake Bell's fourth touchdown run, a 6-yarder with 51 seconds left.
The Bears then went 80 yards in five plays, with Griffin scrambling for runs of 22 and 8 yards before then finding Williams in the back corner of the end zone and throwing before he got knocked down.
``One of the offensive linemen came and told me we just won the game. It was a pretty exciting moment,'' Griffin said. ``We don't consider it an upset. It was good for our team to come out and show the resiliency we have and keep pushing forward.''
The Sooners' loss came a night after Big 12 rival and No. 2 Oklahoma State suffered its first loss, and right after No. 4 Oregon became a two-loss team.
Baylor (7-3, 4-3) had been 0-20 against the Sooners, and most of those games weren't even close.
``At the end of the day, they coached better than we did, and they played better than we did,'' Oklahoma coach Bob Stoops said.
When the game ended, students and fans - most in gold T-shirts - stormed the field to surround Griffin and the Bears after arguably the biggest win in school history.
It was the highest-ranked team Baylor defeated since winning 20-13 at third-ranked Southern California in 1985.
``They said we needed that signature win,'' Griffin said. ``We got it.''
Oklahoma had scored two quick touchdowns after halftime to take a 24-17 lead, then Baylor got a fortunate bounce to get even again
Griffin's pass over the middle deflected off the hands, then the helmet of intended receiver Tevin Reese. The ball went about 20 yards farther down field, and was grabbed out of the air near midfield by Kendall Wright, who sprinted to an 87-yard touchdown.
Griffin dropped to a knee, then looked down before thrusting his arms into the air. The quarterback was shaking his head seemingly in disbelief at what had just happened.
That is how Stoops and the Sooners felt after the game.
Griffin completed 21 of 34 passes while setting single-game school records for passing yards and his 551 total yards. Wright's 208 yards receiving was also a school record, on eight catches.
``Another day at the office for Robert,'' Baylor coach Art Briles said. ``Very talented, very gifted.''
Williams, who had earlier dropped what would have been a touchdown, had five catches for 99 yards. Terrance Ganaway ran for two scores.
Landry Jones completed 36 of 51 passes for 447 yards with an interception. He gave way close to Bell, the freshman short-yardage specialist who had TD runs of 3, 1, 4 and 6 yards.
Even in their first game without injured record-setting receiver Ryan Broyles, Oklahoma finished with 605 total yards. That was 15 fewer than Baylor.
After Trey Millard's 5-yard TD run on Oklahoma's first possession of the second half, Baylor faced fourth-and-1 at its own 33. Griffin took the snap and was stood up in the backfield by David King.
Jones then threw a 31-yard pass to set up Bell's 1-yard keeper that put the Sooners up 24-17 less than 4 minutes into the second half.
When Baylor got the ball back, Williams was behind a defender inside the 10 when he reached up and got his hand on the ball. He looked like he had pulled in as he got close to the end zone, but it suddenly fell to the ground and the Bears punted.
The fortunate bounce came on the next drive, then the Bears went up 31-24 when Griffin hit wide-open tight end Jordan Najvar for a 13-yard TD. That came a play after Williams made a diving 23-yard catch while being grabbed by a defender to convert fourth-and-11.
Ganaway's 11-yard run early in the fourth quarter made it 38-24 before Bell's last two TDs.
Baylor led 17-10 at halftime after a 69-yard TD catch-and-run by Reese, who got wide open several yards behind the Oklahoma secondary. He caught Griffin's pass in stride near the 30 and sprinted to the end zone on the first play after the Sooners had tied the game.
That was Baylor's second quick-strike score in a row, with a long touchdown drive by the Sooners between those.
The Bears needed only 36 seconds for a three-play scoring drive. Wright turned a short crossing pass into a 55-yard gain before Terrance Ganaway had two runs up the middle, for 13 yards and then a 15-yard score.
Oklahoma tied the game with an 11-play, 73-yard drive that ended with Bell's 3-yarder.
The Bears came out throwing deep right from the start. On the second play of the game, there was an 80-yard pass to Wright that would have been an easy touchdown except for the holding penalty that wiped it out. Griffin was pleading with referee for an explanation before Wright had even gotten to the end zone.
Baylor ended up punting, even after penalties helped convert third-and-22 and then third-and-19.
Oklahoma also punted on its opening drive after having a 29-yard TD pass brought back because of an illegal block.
The team traded field goals later in the first quarter before the Sooners lost a fumble at the Baylor 31.