– When she got the ball in her hands, Shayne Mullaney didn’t hesitate. “Coming off two losses, we had a lot of fire in our bellies,” the Gophers senior point guard said Thursday night, after her team’s 82-78 victory over Purdue in its Big Ten women’s basketball tournament opener. “We wanted this really bad.”

After the Gophers frittered away an 18-point lead, Mullaney hit a three-pointer with four minutes remaining to put them back on top — and clutch free-throw shooting kept them there, as they withstood persistent Purdue in a second-round matchup at Sears Centre. The 14th-seeded Boilermakers took a 59-58 lead with 7 minutes, 35 seconds left and stretched that lead to three points.

But the Gophers made 15 of 18 free throws, including six by Mullaney and four by reserve Kayla Hirt, in the final 3:15 to earn a place in Friday’s quarterfinals against No. 3 seed Ohio State.

Coach Marlene Stollings was delighted to see the Gophers earn their 23rd victory of the season, their highest total since 2004-05. Despite some hair-raising moments, she was equally pleased to win her first postseason game as Gophers coach.

The Gophers led 45-32 at halftime, but their cold-second half shooting and outstanding performances by Purdue’s Whitney Bays and Liza Clemons turned it into a tight, tense game. Shae Kelley led the Gophers with 26 points, while Big Ten Player of the Year Amanda Zahui B. scored 21 points and pulled down 11 rebounds before fouling out with 37 seconds remaining. Foul trouble limited Zahui to 13 minutes in the second half.

Bays scored a game-high 28 for Purdue, and Clemons added 19. The Boilermakers performed even better at the line on the night, making 25 of 29 attempts.

“Everyone played their souls out,” said Zahui, who was exhorting her team from the bench in the final minutes. “They never gave up. Everyone wanted to win this game. We’ve been talking about this; we really wanted to advance. You could see it in everybody.”

The Gophers were eager to right themselves after ending the regular season with losses at Nebraska and Iowa. They tore through a 22-4 run midway through the first half to build a 28-10 lead. But the Gophers got sloppy, committing a rash of turnovers and hoisting poorly chosen shots as Purdue tightened its defense. The Gophers failed to score during a 6:03 span, and their lead dwindled to seven before they pulled themselves together late in the half.

Zahui and Kelley combined to score their last 12 points of the half, capping it with an 8-2 spurt for a 13-point halftime advantage. In the second half, the Gophers again let their feet off the gas, as lax defense and cold shooting provided the fuel for the Boilermakers’ rally.

The Gophers missed five of their first six shots of the half and made only nine of 32 in the final 20 minutes. A 15-5 Purdue run cut the Gophers’ lead to 50-47, as Bays and Clemons led the charge. A Bays jumper gave Purdue the lead with 7:35 left, its first lead since 41 seconds had elapsed.

“We got relaxed a little bit on defense,” Kelley said. “And we made mistakes [on offense]. When we were patient, we got what we wanted. We needed to slow down and stay poised.”

The Gophers won it at the free-throw line, with Mullaney’s three-pointer the last field goal they made. Hirt, a 66.7 percent free-throw shooter, came off the bench to score eight points in the second half, including four consecutive free throws in the final 28 seconds to keep the Boilermakers from getting a chance to tie.