Trailing by 19 points eight minutes into the Las Vegas Invitational championship game, the 11th-ranked Spartans (5-1) took the lead in the second half and pulled away for a 78-68 victory on Friday.
Langford scored 29 points, while Winston, who had 20 points and 10 assists, was named the tournament MVP.
"That start, we were just throwing it to them," Michigan State coach Tom Izzo said. "We got to figure why (that start happened). We learned a good lesson. What was good (was) to play against a team like that, Josh to play a second half like that and Cassius to play that good, and the ball screen defense was good. But we got a long way to go."
Texas (5-1) went ahead 25-6 early, but the Spartans cut it to 44-36 at halftime. Michigan State took its first lead on Langford's 3-pointer with 15:26 remaining and went ahead for good on a 3-pointer by Winston 1:19 later.
Michigan State, which had the majority of the fan support, slowly built its lead to 71-59 with 3:32 remaining. The Spartans shot 55 percent from the field in the second half.
"Texas threw their punches and their jabs and we ate them," Winston said. "They made their run and we said, `We are going to push it.' We weren't ready for that kind of pressure. Credit to the team, we just did a good job regrouping."
"In the second half, we got away from who we want to be," Texas coach Shaka Smart said. "We have to do a better job of who we want to be. When you get down, you play with a more ruthless type of approach. I thought Michigan State did a good job after we took that lead."
Michigan State now leads the all-time series 6-4 and has won three straight. The Spartans have reached the championship game in their last six invitational tournaments, winning three.
NO. 7 NORTH CAROLINA 94, NO. 17 UCLA 78
North Carolina trailed for most of its game against UCLA, but with a potentially disastrous trip to Las Vegas looming, the seventh-ranked Tar Heels kept being aggressive offensively -- and it paid off.
Kenny Williams scored 15 points as five Tar Heels reached double figures and North Carolina (6-1) settled for a split in its Las Vegas trip after losing to Texas on Thursday.
"We were effective defensively with our intensity," said North Carolina coach Roy Williams, whose Tar Heel teams had lost three straight in Las Vegas. "We didn't have as many turnovers today. We didn't guard the 3-point line that we wanted to. It was a big game in that we have three teams in the top five or six in our next five games. We played better today."
Kris Wilkes led UCLA (4-2) with 22 points as he converted 7 of 10 from the field. Jaylen Hands added 14 points and nine assists, while Cody Riley had 11 points and nine rebounds for the Bruins, who lost both Las Vegas games.
Thanks to 53 percent shooting in the second half, North Carolina took the lead for good, 63-62, on a dunk by Little with 11:58 left in the game.
UCLA freshman center Moses Brown fouled out with 7:40 left. He finished with seven points and four rebounds.
"He's got to learn," said UCLA coach Steve Alford, whose team lost to Michigan State late Thursday. "He's got to learn and look at this tape. We need him out there for 22 minutes, not eight minutes."
Despite both teams playing two games within 20 hours, both shot well from the field, especially from 3-point range. North Carolina was 30 of 60, including 11 of 23 from 3-point range, while the Bruins were 10 of 22 from 3-point range.
White got into trouble committing his fourth foul with 7:10 left, but Leaky Black, who had five points, filled in nicely.
"Leaky was huge for us," Williams said. "Leaky made some big shots. He still needs more time on the court."
UCLA started quick, hitting its first six shots and never trailing in the first half. The Bruins' largest advantage was 11 with 7:33 left in the half. UCLA finished the half shooting 52 percent from the field and led 46-41 at intermission.
"After getting smacked last night, I thought we responded really well," Alford said. "But when Carolina tightened things up, we didn't handle that well. We now have four games at home, and we got to learn to get better."
The Bruins host Hawaii next Wednesday.
North Carolina now leads the all-time series 9-3 in a game between teams that have combined for 18 national championships.
This is the teams' third meeting in five years. North Carolina defeated UCLA in 2015 at Brooklyn, 89-76, and 2014 in the Bahamas, 75-65.
Cameron Johnson went over the 1,000-point mark in the Tar Heels' loss to Texas on Thursday. He is the 77th Tar Heel to reach the mark.
More AP college basketball: https://apnews.com/Collegebasketball and https://twitter.com/AP-Top25