WEST LAFAYETTE, Ind. -- When a college basketball team has won an NCAA tournament, it obviously knows how to perform on center stage.

Third-ranked Villanova showed that necessary grit and mental toughness Monday night, sinking its first seven second-half shots during a 17-6 run and held off hard-charging No. 15 Purdue 79-76 in sold-out Mackey Arena.

Boilermakers guard P.J. Thompson's halfcourt shot at the first-half buzzer pulled Purdue into a 39-39 tie, but instead of being rattled by a wild crowd, the 2016 national champions reacted as they expect to react in pressure situations.

"That's where the leadership comes in," Villanova coach Jay Wright said. "With Josh Hart and Kris Jenkins, I didn't have to say a lot at halftime. Those guys took control. Josh just said to me at the beginning of the second half, 'We got this.' That's the real strength of this team -- the leadership."

Villanova guard Jalen Brunson sank four clutch free throws during the final 23.2 seconds, and the reigning national champions survived. The Wildcats were 18 of 22 from the line, and Purdue was 12 of 19.

Preseason All-American Hart led Villanova (2-0) with 24 points, Darryl Reynolds added 12 and Eric Paschall scored 11.

"The first five minutes of the second half was the difference in the game," Purdue coach Matt Painter said. "Then, we had to fight back. I think it would have been a different game had Isaac Haas been able to play more in the first half."

Haas, who was saddled with foul trouble, led Purdue (1-1) with 22 points and Caleb Swanigan added 20 for Purdue, which now is 0-6 all-time against top-five nonconference opponents in Mackey Arena, which opened in December 1967.

After Brunson made two free throws with 12.1 seconds to go for a 79-76 lead, the Boilermakers had two 3-point shots in the final 10 seconds, but Swanigan and Carsen Edwards each misfired.

"In the second half, I just liked how we responded to adversity," Hart said. "It was a crazy environment, and every time we did something, they came back with a run. We opened up a little lead, and they came back. The biggest part for us was handling the adversity."

Haas and Swanigan combined to score Purdue's final 17 points, but it was not enough to beat Villanova.

"This game was huge for us, playing a great team and a very disciplined team in this crazy environment," Hart said. "We knew last year was over before this season even began."

Hart's driving layup with 4:09 remaining gave Villanova a 71-67 lead after a Haas dunk had closed the Wildcats' lead to 69-67 at the 4:34 mark.

The Wildcats had taken a 56-45 lead on Hart's three-point play at the 15:52 mark. But with Haas and Swanigan each contributing five points, the Boilermakers quickly crawled back to within 61-60 with 11:06 to play.

Thompson's halfcourt shot at the halftime buzzer pulled the Boilermakers into a 39-39 tie through 20 minutes after Villanova had led 28-18 with 7:11 left in the half.

Purdue battled foul trouble in the early going, and then Haas was whistled for his third with 5:40 remaining in the half and the Wildcats leading 29-22.

Swanigan, who had two early fouls, returned and scored six points late in the half to help Purdue get back into the game.

"We ran the game in the second half, but because of fouls, we weren't able to do that in the first half," Swanigan said. "I knew the only way (Villanova) could play with us was foul trouble, and that it what happened."

Swanigan had 13 points and four rebounds during the first 20 minutes, making 6 of 8 field-goal attempts. Vince Edwards had eight points, three rebounds and six assists before intermission, when Purdue shot 46.7 percent (14 of 30), including a pair of 3-pointers from Thompson.

"In the first half, I didn't do what I needed to do," Haas said. "In the second half, our errors hurt us, but they were simple pass and catch things that we will correct."

Hart had 13 points in the first half for Villanova, and Reynolds, who did not score in the Wildcats' Friday night opener, had 10 first-half points and four rebounds.

Villanova shot 48.3 percent (14 of 29) during the opening half and outscored Purdue 8-5 from the free-throw line.

NOTES: With the loss, Purdue dropped to 38-2 in November home games for coach Matt Painter, the only previous loss being against Bucknell in 2012. ... The Wildcats are 3-0 against the Boilermakers, also winning 67-50 in the 1995 Wooden Classic in Anaheim and 89-81 in overtime in New York City in 2012. ... F Caleb Swanigan had 23 points, 20 rebounds and six assists in Purdue's season-opening victory against McNeese State. ... Villanova PG Jalen Brunson, an Illinois native, is a player Painter recruited heavily. ... The Boilermakers played without sophomore G Ryan Cline, who is suspended for a summer marijuana arrest, and without sophomore F Jacquil Taylor, who underwent left ankle surgery last week and is sidelined indefinitely.