IOWA CITY – Exhale.

That’s what members of the Iowa basketball team and their fans were able to do Sunday.

Coming off three straight losses, including two tough road defeats to teams with lesser records, and some notable failures at home, and perhaps being on the verge of slipping onto the proverbial “bubble’’ for NCAA tournament consideration, the Hawkeyes needed something good to happen.

They got it. They blew a big halftime lead, but did enough in the final 11 minutes to pull out an 83-76 victory over Purdue at Carver-Hawkeye Arena that keeps them off the bubble and provides some sense of relief heading into the final two games of the regular season.

“Shoot, if we had lost this the world might have ended,’’ Iowa forward Aaron White said with a smile that told you he was being sarcastic.

“Obviously this is a big win, a big game. It was disappointing that we lost three in a row but you’ve just got to keep getting better. I think we fixed the problems that we had. Every team in the league has had a stretch like that.’’

The win gives the 20th-ranked Hawkeyes their second straight 20-win season and assures them of being at least .500 in the Big Ten. Those are two items that always look good on an NCAA tournament resume.

“It seems like we hadn’t won in forever,’’ said sophomore guard Mike Gesell, who made several crucial free throws in the final minute. “It was our first extended losing streak of the season. It just feels good to come out and get a win.’’

As with most of Iowa’s victories in the Big Ten season, it wasn’t easy.

“I think for us it was important to have to fight the way we did,’’ Iowa coach Fran McCaffery said. “We had to take care of the ball. We had to guard. We had to make free throws. We had to play intelligent.’’

The Hawkeyes (20-9, 9-7 Big Ten) seemed to be on their way at halftime. Devyn Marble, who finished with 21 points, five assists and four steals, scored nine points in a 15-5 run to end the half, giving them a comfortable 50-37 lead.

But then Purdue started finding shots for freshman sharpshooter Kendall Stephens and began getting defensive stops of its own. The Boilermakers (15-13, 5-11) outscored the Hawkeyes 27-10 to start the second half and took a 64-60 lead when 7-footer A.J. Hammons speared a lob pass and rammed down a dunk with 11 minutes, 21 seconds to go in the game.

“It was gutcheck time,’’ White said. “It’s 64-60. What’s it going to be? Are we going to have a close game, like other ones? Are we going to execute down the stretch? Are we going to turn the ball over or not get stops?’’

They got stops. Purdue went scoreless in eight straight trips down the floor, spanning more than six minutes, and the Hawkeyes regained the upper hand in some unusual ways.

Iowa center Adam Woodbury threw in a hook shot and White drained a 3-point field goal with 8:07 to go to give the Hawkeyes the lead.

Woodbury is only ninth on the Iowa team in scoring and, as Purdue coach Matt Painter pointed out, White was only 3 for 15 from 3-point range in Big Ten play.

“It’s been that kind of year for us,’’ Painter said.

McCaffery figured those plays did more than just get the lead.

“Both baskets clearly got the crowd involved, which was absolutely critical,’’ he said. “We had a great crowd today and we hadn’t given them much in the second half to cheer about.’’

Marble made a big play with 2:39 to go when he drove to the hoop and scored over Hammons, drawing a foul and upping the lead to 75-70.

But the Hawkeyes still only led 76-74 after Rapheal Davis hit the second of two free throws with 42.6 seconds to go.

From there, the Hawkeyes finished the win at the foul line. Gesell made two free throws with 41.8 left, one more with 25 seconds to go and two more with 0:14.8 remaining. Josh Oglesby dropped in two more with 8.2 seconds showing.

Gesell and White each finished with 15 points and Oglesby added 11.

Davis, who averages just 5.3 points per game, scored a season-high 18 points to lead Purdue and Hammons finished with 16 points, 14 rebounds and four blocked shots.

McCaffery figured it wasn’t so much what the Hawkeyes did in the game as what they didn’t do. They matched a season low with only five turnovers, including just one in the first half. He said that was “huge,’’ especially since they shot just 29.6 percent from the field after halftime.

“You can shoot a bad number but if you’re at least getting shot attempts and not turning the ball over and giving up transition points, you at least have chance to win,’’ White said.