MILWAUKEE -- Come March, college basketball teams live by a simple mantra: Survive and advance.

Saturday night, the Purdue Boilermakers did just that, blowing a 19-point lead in the second half only to steady themselves over the final minutes and hold off Iowa State for an 80-76 victory and a trip to the Sweet 16 for the first time in seven seasons.

"We're up 13 at the half, and you knew they were going to make the run," Boilermakers coach Matt Painter said. "You know they were going to score the basketball. We had to make offensive plays, and obviously we made just enough."

Caleb Swanigan anchored the Boilermakers' efforts, scoring 20 points with 10 rebounds and seven assists. He was a dominant force down the stretch, scoring 12 in the second half, including a rally-killing layup after the Cyclones (24-11) cut the deficit to a point with 2:59 to play.

"Everybody makes a run," junior guard Vincent Edwards said. "It's March, it's Madness. It happens. We've got to be able to withstand it. I'm proud of this whole team and the coaching staff. To be able to withstand that run and be able to hold on to it is unbelievable."

Edwards led Purdue (27-7) with 21 points and 10 rebounds and Isaac Haas added 14 points in 15 minutes. The Boilermakers shot 48.4 percent and knocked down 8 of 26 3-point attempts while going 10-for-15 from the line.

Purdue moves on to Kansas City, where it will face either top-seeded Kansas or No. 9 Michigan State in a Midwest Regional semifinal.

"I'm excited," Swanigan said. "I'm ready to get back to campus and get to work and watch the game tomorrow, Kansas-Michigan State, and see who is left."

Deonte Burton scored 17 of his team-high 25 points in the second half while Matt Thomas scored 20 and Monte Morris added 18 and nine assists for Iowa State (24-11), which shot 50 percent (30-for-60) and made 7 of 23 from distance.

"We were playing for our lives," said Burton, a native of Milwaukee who played his first collegiate season for Marquette. "It was a win-or-go-home. I didn't want to go home. I tried to put everything I could into the game tonight."

The fifth-seeded Cyclones got off to a balky start, making just 3 of 11 attempts as the Boilermakers jumped out to a 15-8 lead.

The Cyclones hit on five of their next six to close the gap, but Purdue hit 17 of 30 shots, including six 3-pointers, to take a 44-31 lead into halftime.

After falling behind by 19, the Cyclones made their move: A 23-7 run, including 12 unanswered, made it a three-point game with 8:02 to play.

Swanigan's jumper stabilized the Boilermakers, who went back ahead by six when Edwards completed a three-point play with 5:59 remaining.

Still, the Cyclones weren't done. A layup and 3-pointer from Burton made it a 68-67 game with 5:08 to go, and Thomas tied it up on a jumper with 3:45 left.

Burton followed with a pair of free throws to give Iowa State its first lead of the night, but it didn't last long: Edwards found P.J. Thompson for a 3-pointer to put the Boilermakers ahead by one, and Swanigan's layup made it 76-73.

"They came back," Iowa State coach Steve Prohm said. "They've got some guys and went up three. ... We didn't rebound well at the end. But, you know, a game like this, you can look back at a lot of difficult things."

Edwards hit a jumper that put Purdue up five, and Ryan Cline forced a turnover, but Purdue couldn't cash in. Burton's driving layup got the Cyclones within a possession with 53 seconds left, but Thompson iced it with a pair of free throws in the closing seconds.

NOTES: Purdue F Caleb Swanigan recorded his 28th double-double of the season, the most among Division I players this year and the most in one season by a Big Ten player. ... Iowa State PG Monte Morris ended his career as the Cyclones' all-time leader in victories (100), games played (140), assists (768) and 11th in points (1,708). ... The Cyclones have lost in the second round in six of their last seven NCAA Tournament appearances. ... Purdue lost in the first round each of the past two seasons and hasn't made it past the first weekend since 2010.