KANSAS CITY Both North Carolina’s best asset and most glaring liability played prominent roles Friday night against Villanova. In the end, the Tar Heels ability to shoot from the perimeter outweighed their inability to rebound, and North Carolina escaped with an 78-71 victory in the second round of the NCAA tournament.

North Carolina coach Roy Williams, who earned his 700th career victory, made the mid-season switch to a smaller, four-guard starting lineup because he believed it would give his team its best chance to be successful. But he also understood that the lineup presented risks – especially against teams with size, and ones that rebound well.

The eighth-seeded Tar Heels’ (25-10) ability to shoot saved them, after they surrendered a 20-point first-half lead. But their inability to rebound effectively nearly doomed them.

No. 9 Villanova (20-14) pulled down 13 offensive rebounds during the second half, and turned them into 17 second-chance points. All of the Wildcats’ second-chance points came in the second half, after they awoke from a first-half slumber that saw them fall behind 32-12 with seven minutes before halftime.

But as good as Villanova was after its own missed shots, UNC was equally so from the perimeter. The Tar Heels made 11 3-pointers – six in the second half – and they made 3s on three consecutive possessions to pull away with about five minutes left.

Still, it wasn’t easy. Villanova kept fighting, and kept coming back.

The game’s decisive stretch began with about 6 1/2 minutes to play, and North Carolina leading by four. P.J. Hairston made a 3-pointer, his second of the second half, to give the Tar Heels a seven-point lead. After a Villanova layup, Reggie Bullock made a 3 from the right corner to put UNC ahead by eight.

The Wildcats responded again, and again UNC answered with a 3 – this one from Hairston with a little more than five minutes remaining. That gave the Tar Heels a 63-54 lead, and prompted Villanova coach Jay Wright to call a timeout.

His team didn’t go away after trailing by as many as 20 points during the first half, and it didn’t go away in the final five minutes, either. Ryan Arcidiacono, the Wildcats’ freshman point guard, rattled in a 3-pointer to cut the Tar Heels’ lead to six with a little than four minutes to play. Marcus Paige, the UNC freshman who has excelled lately in late-game situations, made a jumper to push the Tar Heels’ lead back to eight with 3 minutes, 20 seconds left.

From there Arcidiacono made a pair of free throws to cut North Carolina’s lead to six, and he made a steal that set up James Bell’s 3-pointer, which cut UNC’s lead to three. The Tar Heels faltered late against Villanova’s pressure defense, and turned it over on their next possession, too, after James Michael McAdoo, wide open under the basket, allowed a pass to slip through his hands.

JayVaughn Pinkston, Villanova’s sophomore forward, rebounded a miss on the Wildcats’ next possession, and drew a foul. He made two free throws, and it was a one-point game with two minutes and 14 seconds left.

Paige made a 3-pointer from the left side, though, to put North Carolina back ahead by four with two minutes to go. Villanova’s Mouphtaou Yarou made a layup to trim the lead to two, and then Paige made two free throws to put UNC back ahead by four.

The Tar Heels came up with a stop but Villanova made a steal off an inbounds pass before missing a layup that would have cut UNC’s lead to two with less than one minute to play. Hairston secured the rebound, was fouled, and made one of his two free throws to give UNC a 73-68 lead with 53 seconds left.

After another defensive stop, Paige passed ahead to Hairston, who made a layup while Bell fouled him. He made the free throw to put the Tar Heels up by eight with 42 seconds left.

Hairston led UNC, which shot 49 percent overall, with a game-high 23 points. Pinkston had 20 for Villanova, and McAdoo added 17 points for the Tar Heels. Ten of those came during the first half, which UNC mostly dominated.

UNC led 32-12 with seven minutes to play in the first half. But Villanova outscored the Tar Heels 28-8 during the next 11 minutes and eight seconds to tie the game at 40. That run included the Wildcats’ 8-0 run to close the first half, and their 11-3 run to start the second half.

Having seen enough, UNC coach Roy Williams took out all of his starters with about 16 minutes to play, and replaced them with a lineup of forwards Desmond Hubert, Brice Johnson and J.P. Tokoto, and guards Leslie McDonald and Luke Davis.

It was a move Williams had also used, with success, during the Tar Heels’ home victory against N.C. State. In that game, UNC’s starters received Williams’ message, and finished the game strongly. In this one, the Heels simply hung on, and overcame its biggest weakness with its biggest strength.