ARLINGTON, Texas (AP) — Alex Bauman knew right away he had scored probably the biggest touchdown in Tulane history, even after the true freshman tight end’s contested 6-yard catch at the end of the Cotton Bowl was initially ruled incomplete.

“I kept my hands under the ball,” he said.

The long replay review proved Bauman made the catch with 9 seconds left, even with linebacker Eric Gentry draped over him as they rolled over in the end zone. That capped a frantic finish for the 14th-ranked Green Wave in a 46-45 win over Heisman Trophy winner Caleb Williams and No. 8 Southern California on Monday.

“I might have had a heart attack,” Tulane coach Willie Fritz said on the field moments after the game ended.

“If you told us before the game that we had one drive, one opportunity to go down there and win the game, then we’d take that 10 out of 10 times,” quarterback Michael Pratt said.

The Green Wave (12-2) scored 16 points in the final 4:07, the game-winning touchdown coming after they got the ball back following a safety, to complete an FBS-record 10-win turnaround after going 2-10 last season.

“Huge win for the program, huge win for the university, huge win for the city,” Fritz said.

Williams was 37-for-52 passing for 462 yards and a Cotton Bowl-record five touchdowns, exactly one month after suffering a hamstring injury in USC’s loss to Utah in the Pac-12 championship game that kept the Trojans (11-3) from making the four-team College Football Playoff.

Tyjae Spears ran for 205 yards, his FBS-best eighth consecutive 100-yard game. His career-best fourth touchdown started the final scoring surge for American Athletic Conference champion Tulane, which was in the New Year’s Six game as the highest-ranked Group of Five team.

The Green Wave played in their most significant bowl since the Sugar Bowl on New Year’s Day in 1940, when they were still in the Southeastern Conference, and it was their biggest bowl win since the 1935 Sugar Bowl in New Orleans, where their campus is located.

After Spears’ 4-yard TD run with 4:07 left, the Green Wave opted to kick deep instead of trying an onside kick. Mario Williams signaled for a fair catch, but fumbled the ball out of bounds at the 1. Two plays later, defensive tackle Patrick Jenkins met Austin Jones in the end zone and smothered him for a safety.

“We were debating whether or not to onside kick,” said Fritz, the seventh-year Tulane coach. “Obviously it was great that we got it on the 1 and got the safety.”

Pratt completed only 8 of 17 passes for 234 yards, but had two 24-yard completions on that final drive after the safety. He also scrambled 8 yards on a fourth-and-6 play and finished with 83 rushing yards.

Tulane linebacker Nick Anderson, a former Vicksburg High star, had five total tackles and one tackle for loss.

Pratt’s first 24-yard completion to Bauman converted a fourth-and-10. Deuce Watts then held on despite a crushing hit from a defender that left both of them on the ground after a 24-yard gain to the 6 with 18 seconds left.

After Caleb Williams followed coach Lincoln Riley from Oklahoma, the Trojans matched the biggest turnaround in school history despite the coach’s first loss in six games at AT&T Stadium. Their debut was a seven-win improvement over last season’s 4-8 record.

“I’ve rarely at the end of the year felt so conflicted,” Riley said. “On one hand, sick about the way we finished the season. … We lost three games this year. We lost two of them on the last play of the game. And we lost one in the fourth quarter in the championship game when we had a chance to go to the College Football Playoff.”

The Trojans never trailed until that final touchdown. Williams threw TD passes on each of their first two possessions. A 9-yarder to Michael Jackson III capped the game-opening 9-minute drive, the longest by time for USC this season, and Terrell Bynum’s 3-yard catch capped a 95-yard drive early to make it 14-0 in the second quarter.

Tulane tied the game at 14 on Pratt’s touchdown pass to Jha’Quan Jackson, an 87-yard catch-and-run. But USC scored twice in the final 2:21 of the first half, on Raleek Brown’s 39-yard run and Brenden Rice’s 4-yard catch with 12 seconds left.

Rice, the son of Pro Football Hall of Fame receiver Jerry Rice, had career bests with six catches for 174 yards and two touchdowns. Tahj Washington had five catches for 109 yards.

The Cotton Bowl was Caleb Williams’ third game this season with five TD passes. His only interception set up Tulane’s long game-tying TD. On a scramble with open field in front of him, Williams instead threw off his back foot and was picked off by Jarius Monroe.

“It’s going to linger. You lose the last game of the season, go into the offseason, burns,” Williams said. “Don’t have another game after. It’s going to burn.”