AUSTIN (KXAN) — The No. 8 Texas Longhorns held off quarterback Donovan Smith and the Houston offense to escape with a 31-24 Saturday at TDECU Stadium.

On third-and-1 from the 10-yard line with 1:20 left, Houston running back Stacy Sneed looked as if he made the line to gain, the 9-yard line, for a first down. However, the officials spotted him a half-yard short to set up a fourth down. Smith had been terrific the whole game, and on the pivotal play, his pass to Stephon Johnson fell incomplete and Texas took over with 1:03 left.

With 5:37 left in the game, Texas freshman running back CJ Baxter scored the go-ahead touchdown on a 16-yard run. The score capped a 6-play, 53-yard drive that took 1:53 to break a 24-24 tie.

“I can remember vividly us not winning a game like this a year ago and two years ago,” Longhorns head coach Steve Sarkisian said. “I think it speaks to this team’s mental toughness and their ability to finish in the fourth quarter. I’m happy to know when I wake up tomorrow morning we’ll be 6-1 and not 5-2.”

Texas jumped out to a 21-0 lead in the first half and it looked like they were going to cruise to victory. Quinn Ewers threw a pair of touchdown passes, a 14-yarder to Adonai Mitchell and a 42-yarder to Xavier Worthy, on the first two drives of the game. Savion Red added a 1-yard rushing touchdown with 12:49 in the second quarter, and the rout appeared to be on.

Smith, who had a very good game against the Longhorns while playing at Texas Tech last season, heated up with his team down 21 points. He fired three touchdown passes, two in the second quarter and one early in the third, to get the Cougars back in the game. Smith found Matthew Golden twice and Joseph Manjack IV as the Cougars clawed their way back.

The comeback was helped by a fake field goal attempt gone awry by Texas in the second quarter. Ryan Sanborn, the holder on the field goal team and punter, threw a pass to kicker Bert Auburn on fourth-and-6 that gained just one yard. Smith and Houston matched down the field and scored on the ensuing drive to cut into Texas’ lead 21-14.

Sarkisian said that was “a poor call,” and that the team let its foot off the gas pedal.

“We’ve got to have a killer instinct and people aren’t going to lay down against us,” Sarkisian said. “We relaxed and didn’t execute the way we had, and they got some momentum from the fake field goal.”

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Smith finished the game 32 of 46 passing for 378 yards and three touchdowns and an interception. Texas’ Michael Taaffe made a big play with an interception in the end zone with 12:41 left in the fourth quarter.

Houston was one-dimensional on offense yet still almost pulled off the upset. Of their 392 total yards of offense, only 14 came on the ground. Houston had 20 first downs to Texas’ 19.

Ewers finished the game 23-for-29 for 211 yards and a pair of touchdowns but left the game after taking a big shot on a scramble late in the third quarter. Sarkisian said Ewers injured his shoulder and he’ll know more about the severity of the injury Sunday.

“He tried to play through it, but we didn’t feel comfortable enough with his ability to play, so that’s when Maalik (Murphy) went in the game,” Sarkisian said.

Murphy played the entire fourth quarter and completed one pass for seven yards.

Jonathon Brooks finished with 150 all-purpose yards on 28 touches. His streak of consecutive 100-yard rushing games ended at four after he gained 99 yards on 20 carries, but he added 51 receiving yards on eight catches. Xavier Worthy turned in a nice game with 92 yards on six catches.

Texas (6-1, 3-1 Big 12 Conference) is home next week against another Big 12 newcomer, BYU. The game is scheduled to start at 2:30 p.m. and be broadcast on either ABC or ESPN. Houston (3-4, 1-3) hits the road to The Little Apple, Manhattan, Kansas, to take on the Kansas State Wildcats next week.