SAN ANTONIO -- A thrilling, back-and-forth, record-shattering Alamo Bowl had barely ended when Heisman Trophy winner Robert Griffin III already started hearing the chants.

"One more year! One more year!"

One more year? There's still the craziness of what happened Thursday night to get through first.

Griffin wasn't dazzling in possibly his last college game -- and didn't need to be -- yet Baylor still pulled out an incredible Valero Alamo Bowl victory in the highest-scoring regulation bowl game in history, beating Washington 67-56 in the wildest shootout of this bowl season or any other in memory.

If this was RG3's final showcase before jumping to the NFL, it was a gripping goodbye to watch. One of the nation's most electrifying players was upstaged by an even more exciting nail-biter that shattered the previous record for points in regulation set in the 2001 GMAC Bowl.

"We went out in style!" Griffin shouted to his teammates. He paraded the Alamo Bowl trophy around the field before taking it to the front row of the stands and his mother, who's already been looking at her son's NFL draft prospects.

Griffin said he was still catching his breath after this one.

"I want Baylor nation to enjoy this," Griffin said. "It's not about me. I've got about two weeks. I'll enjoy this the next day, and then the next day, and then I'll make it."

The previous bowl record for a regulation game was 102 total points set in the 2001 GMAC Bowl between Marshall and East Carolina. That game went to double overtime and ended with a combined 125 points -- which still stands as the overall bowl record.

Baylor, which won its first bowl game since 1992, and Washington (7-6) also set a bowl record for total offense in a game with 1,397 yards.

Griffin had an unremarkable night, throwing just one touchdown pass and running for another. But Terrance Ganaway starred ably in his place, rushing for 200 yards and five touchdowns. His last was a 43-yard run with 2:28 left to seal Baylor's first 10-win season since 1980.

Washington quarterback Keith Price outplayed his Heisman counterpart, going 23 for 27 with 438 yards and four touchdowns. He also ran for another three scores.

"I think we'll have a hard time this bowl season to see a quarterback play as well as he did," Washington coach Steve Sarkisian.

Griffin was 24 of 33 for 295 yards -- and his only touchdown throw came on the game's opening drive.

Blown out in four other games against ranked opponents this season, the Huskies finally made one interesting. Not that it started that way after Baylor ran up 245 yards of offense alone in the first quarter -- awful even by the standards of Washington's defense, which is among the nation's worst.

Then the most award-winning QB in the country suddenly stopped looking like even the best one in the Alamodome.

Price, a sophomore who threw a school-record 29 touchdowns in his first year as the starter, began cutting into a 21-7 deficit with a 12-yard scoring strike to James Johnson. Seven minutes later he tied the game when Devin Aguilar somersaulted over the goal line after catching a 1-yard lob.

The overwhelming crowd of Baylor fans -- decked in green-and-gold Heisman shirts and armed with signs such as "Superman wears RG3 socks" -- stood in stunned silenced. That gave way to disbelieving gasps on the next series, when the typically sure-handed Griffin fumbled after getting popped by Andrew Hudson.

After that, it was practically a free-for-all of big plays.

A 56-yard touchdown dash by Chris Polk. An 80-yard touchdown catch by Washington's Jermaine Kearse two plays into the second half. An 89-yard scoring rumble by Baylor's Terrance Ganaway. Kearse again, catching and darting for 60 yards before getting dragged down, setting up Price's fourth touchdown toss the next play.

Back and forth, back and forth. One after another. In all, five plays covered 50 or more yards, three of them for scores.

"That was crazy," Baylor coach Art Briles said.

For an Alamo Bowl short on drama and light on matchups in recent years, it was a thrilling scoring spree that overshadowed the mere novelty of featuring the Heisman winner. And that in itself was a rarity for a bowl of this stature: Not since Ty Detmer took BYU to the Holiday Bowl in 1990 had a Heisman winner played in a bowl before New Year's Day.

Plenty came to see this one.

Anticipating a surge of Heisman gawkers, Alamo Bowl officials added 800 temporary seats and opened up others with obstructed views that required ticket-buyers to sign a form acknowledging the poor sightlines. Those seats sold, anyway, and the announced attendance of 65,256 was the fifth-largest in the bowl's history.

Others had better seats.

That includes Miami Dolphins general manager Jeff Ireland, who kicked for Baylor in the late 1980s but was here on business scouting Griffin in case the fourth-year junior enters the draft. Griffin's parents, two sisters and fiancee watched the nail-biter with front-row seats.

Griffin acknowledged this week his parents are looking at his draft prospects but denies having any substantial talks with them.

Win or lose, it was an impressive finale for Washington after stumbling into the postseason losing four of its last six. Particularly against a ranked team after then-Top 25 opponents Nebraska, Stanford, Oregon and USC all crushed the Huskies by an average of 24 points.