Tulane linebacker Nico Marley, left, and Edward Williams, right, sack Houston quarterback Greg Ward, during the first half of an NCAA football game at TDECU Stadium, Saturday, Nov. 8, 2014, in Houston. (AP Photo/Houston Chronicle, Cody Duty)

HOUSTON — Hearts were in throats. Hands were on heads.

Tulane had watched its 14-point cushion shrink to just 5 yards as Houston was rolling toward its second touchdown in a minute, with overtime looming.

The Green Wave traded nerves for jubilation a few seconds later when Parry Nickerson intercepted a pass in the end zone as time expired to seal a 31-24 victory at TDECU Stadium. The win gave the Green Wave a signature moment in its first season in the American Athletic Conference.

“I need a defibrillator,” center Nathan Shienle said. “That was crazy.”

Kicker Andrew DiRocco’s 25-yard field goal extended Tulane’s advantage to 31-17 in the final four minutes, but Houston didn’t stop coming. The Cougars (5-4, 3-2) drove 82 yards in 12 plays, capped by a 9-yard touchdown pass to Deontay Greenberry.

That shook up Tulane (3-6, 2-4). Then Houston nearly knocked the Green Wave off its feet.

An onside kick bounced off the chest of Lorenzo Doss and was recovered by the Cougars at their 47 with a minute left. Houston quarterback Greg Ward Jr. used his arm and legs to push the Green Wave back until defensive tackle Tanzel Smart pressured Ward into the pass that ended in Nickerson’s diving arms.

Tulane’s bench spilled out onto the field, and teammates carried the redshirt freshman cornerback from West Jefferson High halfway to the locker room, where an unabashed party broke out as Tulane won its first game outside of Louisiana since beating UAB 44-10 in September 2011.

“I just about passed out,” defensive end Royce LaFrance said. “I can’t believe that just happened.”

Neither could most of the 32,205 in TDECU Stadium, which witnessed Houston’s homecoming coronation end in its first loss to Tulane since 2002. The three-touchdown underdog snapped a 10-loss skid to the Cougars.

Powered by Tanner Lee’s 237 passing yards and three touchdowns, the Green Wave offense operated smoothly and efficiently with the exception of an implosive two minutes at the end of the first half.

Freshman running back Dontrell Hilliard piled up 192 all-purpose yards and two touchdowns after being thrust into the starting lineup by injuries to Sherman Badie and Lazedrick Thompson. He teamed with Lee to piece together Tulane’s most complete offensive performance of the season. After averaging just 11.6 points in its past six games, Tulane tallied 31 against the stingiest defense in the AAC.

“It started with the way we handled the first half,” Hilliard said. “We came out and did what we were supposed to, and I knew all the way we could win this game.”

Tulane took full advantage of good field position to start the game. Unlike in last week’s 38-14 home loss to Cincinnati, when a game-opening interception was followed by being stuffed at the goal line, the Green Wave used Nico Marley’s forced fumble to jump to a 7-0 lead. Lee directed a 26-yard drive, capped by a perfectly thrown touch pass to Teddy Veal in the corner of the end zone from 12 yards, staking Tulane to an early advantage.

Tulane had a chance to pounce even harder when Sam Scofield’s interception set up the Green Wave’s next possession at the Houston 36, but Lee was sacked for an 11-yard loss on the first play, knocking the Green Wave out of field goal range.

Ward directed a 13-play, 93-yard drive and converted three third downs, overcoming two holding penalties along the way. When Ward hit Markeith Ambles on a slant, it allowed the senior receiver to do a front flip into the end zone, tying the score at 7.

But Tulane bounced back with a big play of its own midway through the second quarter, when Hilliard got behind the Houston secondary and hauled in a 63-yard touchdown pass.

A few defensive stops later, it appeared Tulane was headed toward a halftime lead. Then disaster struck.

With barely more than two minutes remaining, the Green Wave started a drive at its 7-yard line, throwing a safe out route to Veal. The freshman hauled in the catch for 4 yards but coughed up the ball. A scrum pushed it into the end zone, where Houston’s Adrian McDonald recovered to tie the score at 14.

Ninety seconds later, Lee’s overthrown pass was hauled in by McDonald for an interception and, three Ward completions after that, Kyle Bullard chipped in a 39-yard field goal, sending Houston to the locker room with an improbable 17-14 advantage.

Unlike in previous games this season, Tulane didn’t melt down after that series of errors. Instead, it rose to the occasion.

“Everyone was saying the right things and that meant a lot, I felt,” Doss said. “We knew it wasn’t going to be easy, but we were right in the game and nothing was too far gone. We came out and did what we said.”

Doss lived up to his words, racking up a third-down sack on the opening drive of the second half to push Bullard into a 49-yard field-goal attempt. He pushed it to the right, keeping Tulane’s deficit at just three points.

Lee then cobbled together a 12 play, 84-yard drive and converted four third downs along the way. He pinpointed four true freshman receivers, including a 9-yard touchdown to Leondre James on a fade pattern.

He followed with more of the same, marching 80 yards in 12 plays on the next possession, capped by Hilliard’s 1-yard touchdown run to set up the late-game drama.

Now Tulane will try to capitalize on the momentum, hosting Memphis for the first homecoming in Yulman Stadium next Saturday.

“It’s been difficult to go to practice every week, and every week it seems like we mess it up or turn it over or do something silly,” coach Curtis Johnson said. “Now we finally put something together and finally did enough to beat a really, really good team.”