GLENDALE, Ariz. -- As North Carolina missed four consecutive free throws in the final 5.8 seconds, coach Roy Williams had one thought.

"Jump off the building," he said.

No need.

The Tar Heels might have had a tough time shooting Saturday night, but showed why they are the best rebounding team in the country at exactly the right time.

North Carolina twice rebounded its missed free throws in the final seconds with center Kennedy Meeks coming up a game-clinching board as the Tar Heels finally subdued Oregon 77-76 in a cold-shooting Final Four game Saturday at University of Phoenix Stadium.

"We're relieved," Williams said. "We feel very lucky."

But it doesn't seem like luck that North Carolina will be playing for the national title for the second consecutive season after losing in the 2016 championship game on Villanova's last-second shot. It will be a matchup of No. 1 seeds in Monday night's final as the Tar Heels (32-7) take on Gonzaga (37-1).

Meeks dominated inside against the smaller Ducks, scoring 25 points on 11-of-13 shooting. He had 14 rebounds, including eight off the offensive glass.

He missed two free throws with 5.8 seconds left, but wing Theo Pinson batted the rebound out to point guard Joel Berry II, who was fouled with four seconds to go. He also missed both attempts, but Meeks grabbed the board and North Carolina ran out the clock.

"Yeah, we needed to get a rebound there," Oregon coach Dana Altman said.

"We had our opportunity. We had some really bad turnovers and made some really bad decisions with some really quick 3s. I thought we were pressing a little bit with guys trying to make plays, but I can't fault our competitiveness."

North Carolina led the entire second half as neither of the Ducks' two big scorers -- forward Dillon Brooks and guard Tyler Dorsey -- could get hot enough to make it a one-possession game until the final minute.

Dorsey hit a 3-pointer that rolled around the rim to bring the third-seeded Ducks within 77-74 with 42 seconds left.

Pinson missed a driving layup, and Oregon pushed the ball the other way, bypassing a 3-point shot for an easy layup by center Keith Smith with 6.4 seconds left to make it 77-76.

And then North Carolina, which entered with a national-best rebounding margin of 13, held on.

"We caught them on a night they didn't shoot the ball very well," Williams said of Oregon.

North Carolina forward Justin Jackson poured in 22 points, including four 3-pointers. But the Tar Heels shot 36.8 percent, which allowed Oregon to hang around.

Brooks, the Pac-12 Player of the Year, finished with 10 points on 2-of-11 shooting before fouling out with 1:32 to go.

Dorsey, who made 25 of 40 3-point shots in the past six games, scored 21 points. He was 3 of 11 from the field and 12 of 12 from the line.

Oregon (33-6) shot 37.9 percent, including 7 of 26 from behind the arc, and it committed 16 turnovers. But the Ducks had enough moxie to trim a 10-point deficit with 8 minutes to go to one in the final minute.

"I wish there was something I could say to make them feel better," said Altman, whose team made the Final Four a year after reaching a regional final. "It hurts. Those guys are great competitors. I thought that was the greatest characteristic they had and we showed some of that tonight. They wouldn't give in."

Neither team looked in sync early.

North Carolina made three of its first 17 shots from the field, but Oregon failed to take advantage because it committed six turnovers in the first seven minutes.

Brooks was 0 of 4 from the field with four turnovers at one point. Dorsey missed all four of his field goal attempts in the first half. North Carolina forward Isaiah Hicks finished 1 of 12 from the field. Berry was 2 of 14.

Meeks, however, was a constant.

"I just knew we had to be aggressive in the paint," he said. "Coach told us it was going to be a man's game. ... I took it upon myself to try to do the best I could to call for the ball."

NOTES: North Carolina made its record 20th appearance in the Final Four. ... The Tar Heels' Roy Williams coached his 99th NCAA Tournament game. He is 75-24. ... Oregon C Jordan Bell had 13 points and 16 rebounds, his sixth consecutive NCAA Tournament game with at least 12 rebounds. ... North Carolina C Kennedy Meeks posted his 13th double-double of the season. He has 148 offensive rebounds this season, moving him into second on the UNC single-season list behind Tyler Hansbrough (151 in 2008). ... The attendance of 77,612 was the second-highest total for a Final Four. ... The Tar Heels won five national titles, most recently in 2009.