Carter sank two free throws with 1 second left in overtime to lift No. 18 West Virginia to an 86-85 victory over TCU on Saturday.
Teammate Jaysean Paige bearhugged Carter after the final horn sounded, and West Virginia's players carried Carter off as fans stormed the court.
"I've been dreaming that my whole life," Carter said. "When I was a little kid, I had the thought. It was always going to be a big game with no time remaining on the clock and I got to the line and go to the free throw line to make two shots and win the game."
Thanks to the freshman, West Virginia (16-3, 4-2 Big 12) narrowly avoided another meltdown after falling 77-50 at No. 17 Texas a week ago.
Carter had already come up big for the Mountaineers earlier this season. The reserve guard scored 28 points in a win over VMI and entered Saturday's game as the best free-throw shooter (79 percent) on a team averaging only 67 percent from the line.
West Virginia made 6 of 8 free throws in overtime after going 16 of 24 in regulation.
TCU led 80-75 after a Kyan Anderson jumper with 1:16 left in overtime, but Daxter Miles Jr. hit 3-pointers 21 seconds apart to put West Virginia ahead 84-83 with 8 seconds left.
After TCU's Trey Zeigler made a basket in the lane with 2 seconds left, Carter missed a layup but was fouled by Anderson on the drive.
Carter said he initially thought he cost his team a chance to win the game.
"Then I looked at the ref and he had his hand up and I was like, `Thank the Lord," Carter said.
Carter said teammate Juwan Staten gave him some encouragement before the free throws.
"He said, `You're the best shooter on this team," Carter said. "You're going to go to the line and win this game."
Anderson scored 22 points to lead six players in double figures for the Horned Frogs (14-5, 1-5).
TCU had a chance to match the number of league wins (2) it had in the past two seasons combined. The Horned Frogs held a 47-37 rebounding advantage and made 5 of 6 field goals in overtime but missed three free throws in the final minute.
"We had opportunities from the free throw line and we didn't get it done," said TCU coach Trent Johnson. "This is one thing about athletics that I really struggle with. These losses are really hard.
"We need to regroup."
In regulation, TCU came from eight points down in the final nine minutes, with Zeigler's turnaround jumper in the lane giving the Horned Frogs a 72-70 lead.
Miles hit a layup with 1 second left, and TCU turned the ball over on the subsequent inbounds play without any time ticking off the clock.
Staten then inbounded to Williams, who had his back turned to the basket and missed an off-balanced short shot at the buzzer.
West Virginia: The Mountaineers won their sixth straight against the Horned Frogs and swept the season series. ... Coach Bob Huggins earned career win No. 756 and moved into 13th place ahead of Henry Iba among major college coaches. Western Kentucky's Ed Diddle is 12th with 759 wins.
NO MORE SLUMP
Staten had 12 assists, made 10 of 15 free throws and broke out of two-game slump. He had seven points in his previous two contests on 2-of-16 shooting,
"I told everyone before the game that he'd have a great game," said coach Bob Huggins said. "The way he shot yesterday and today I thought he would have a lot of confidence and he did. He's got a lot of confidence in the team."
TCU: Hosts No. 11 Kansas on Wednesday.
West Virginia: at Kansas State on Tuesday.
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