Austin, Texas ? The 13th-ranked Longhorns showed they can gut out a big win — and with a freshman leading the way.

Vince Young shook off a sore right ankle to rally the Longhorns with his running and passing and scored the winning touchdown from a yard out on fourth down with five minutes left as No. 13 Texas beat No. 16 Kansas State, 24-20, Saturday.

The Longhorns (4-1, 1-0 Big 12 Conference), whose reputation suffered after a 38-28 home loss to Arkansas Sept. 13, will face No. 1 Oklahoma next week in Dallas.

“We needed a tough win,” Texas coach Mack Brown said. “We needed a come-from-behind win. I’m proud the guys did what they needed to do to win.”

What the Longhorns needed was someone to make big plays late to steal momentum and win the game. They got it all from Young.

The backup to starter Chance Mock in Texas’ quarterback rotation, Young led Texas to a second-quarter field goal on his first drive, but limped off the field in pain after rolling his ankle on a sack in the third.

He returned in the fourth and led Texas to the winning score after Mock had little success moving the nation’s highest-scoring offense.

Young’s fourth-down dive over the top of the line capped an 88-yard drive that started after Texas recovered Kansas State quarterback Ell Roberson’s fumble.

The big play in the drive came when Young uncorked a 52-yard pass to Tony Jeffery, who scored the game’s first touchdown on a blocked punt in the first quarter. Jeffery went over cornerback Cedrick Williams to make the grab, and Young scored five plays later.

Texas wide receiver Sloan Thomas catches a 51-yard touchdown pass in the second quarter against Kansas State. The Longhorns won, 24-20, Saturday in Austin, Texas.

“We always knew Vince could run the football, but he went out there and made plays today,” said Texas receiver Roy Williams.

For Kansas State (4-2, 0-1), the Wildcats’ second straight loss labels them once again as a pretenders for the national title and knocks them completely out of the chase.

“It was a devastating loss,” linebacker Bryan Hickman said. “It was probably the biggest game of the season.”

Roberson’s fumble marred what was almost a spectacular return for the quarterback who missed K-State’s loss to Marshall because of a hand injury.

Roberson ran for 87 yards and two touchdowns — including a one-yard run that gave the Wildcats a 20-17 lead. But he also had three turnovers with two interceptions, including one in the end zone that killed a scoring chance late in the first half.

Roberson’s spinning, weaving 27-yard touchdown run in the third cut Texas’ lead to 17-10 and a long completion to James Terry set up the second score.

But just when the Wildcats looked to put the game away after getting a fumble deep in Texas territory, the momentum turned on Roberson’s fumble.

“It was down there for the knockout,” Roberson said. “I just fumbled the ball. There are no excuses.”