TCU, which had won an FBS-best 25 consecutive regular-season games, overcome a 47-23 deficit in the fourth quarter to briefly take the lead. New starting quarterback Casey Pachall threw three touchdowns passes in the rally and a fumble by Bears quarterback Robert Griffin set up a go-ahead 27-yard field goal by Ross Evans, who earlier missed twice from behind 40 yards.
But Baylor, which hadn't beaten a ranked team since 2004, then went 60 yards in 11 plays -- including Griffin's 15-yard catch from Kendall Wright on a third-and-10 -- to set up Jones.
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The Frogs had one more chance, but Pachall's last pass was intercepted by Mike Hicks and he ran the clock down to 2 seconds in Baylor's most-anticipated opener in a long time.
Griffin took one more snap, knelt down and immediately the field was swarming in gold as students and fans rushed out to celebrate. Many of those in purple sat in the stands staring out in shock.
Wright threw for a score of his own before catching two of Robert Griffin's career-high five touchdown passes as Baylor avoided another crushing loss to the defending Rose Bowl champion and its old Southwest Conference rival.
This would have certainly hurt more than the Bears' 45-10 loss in Fort Worth a year ago because Baylor was never in that game.
Griffin hit 21 of 27 passes for 359 yards, with Wright catching 12 of them for 189 yards. Terrance Williams had six catches for 126 yards and two scores.
This is not the same TCU team that was a BCS buster the last two seasons. There are missing pieces on a defense that finished the last three seasons No. 1 overall in the country, and four-year starting quarterback Andy Dalton is now a rookie starter in the NFL.
Pachall was 25 of 39 for 251 yards and four TDs with that one interception. He threw to 10 players, with Josh Boyce making nine catches for 96 yards.
The only time Baylor really appeared to be going backward before TCU's big comeback was when Wright was excitedly backpedaling after throwing his pass, a 40-yard touchdown to Williams only 2 1/2 minutes into the game. Wright took a quick pass behind the line from Griffin, drawing the defender and leaving Williams wide open.
TCU allowed only 229 yards per game last season, and the most allowed in the regular season was 361 by SMU. The Bears had 360 at halftime, when they led 34-23, and finished with 564.
It was the most yards and points allowed by the Horned Frogs since Sept. 24, 2005, in their 51-50 overtime victory over BYU, which had 614 yards.
Baylor was 0-4 against Top 25 teams last season, when the Bears finished 7-6 with a bowl appearance for the first time since 1994. Their last win over a ranked team was a double-overtime victory over No. 16 Texas A&M in 2004.
Griffin is back for his fourth year, though he is only listed as a junior after a hardship redshirt for that early season-ending knee injury in 2009.
Baylor built a 40-23 lead when Griffin appeared to underthrow Lanear Sampson streaking down the left sideline. But cornerback Greg McCoy, who had some big kickoff returns for the Frogs, misplayed the ball and Sampson caught it for a 64-yard touchdown.
Griffin's fifth TD pass came on the next drive, a 42-yarder to Williams. And even that wasn't enough.
Pachall, the sophomore who threw only nine passes behind Dalton last season, threw two TDs in a span of 3:18 early in the fourth quarter.
The Frogs drove 80 yards on 14 plays before Pachall threw a 1-yarder to Logan Brock. Skye Dawson's 30-yard punt return and a 15-yard penalty then set TCU up at the 12 before Pachall had a 9-yard TD throw to Boyce and they then connected for 2-point conversion.
After a short punt set TCU up at midfield, Pachall threw a 19-yard TD to David Porter. But another 2-point try to Boyce was incomplete.
Stansly Moponga caused and recovered a fumble by Griffin at the end of the 10-yard run that started the ensuing Baylor drive.
For Gary Patterson, TCU's defensive-minded coach, and new Baylor defensive coordinator Phil Bennett, the opener certainly couldn't have been too enjoyable.
During one span in the first half, there were scores on six consecutive possessions - three touchdowns by Baylor and two touchdowns and a field goal for TCU. Griffin threw TD passes of 35 and 27 yards to Wright during that span, and Pachall had a 23-yarder to Brock.