NEW YORK — Dayton should be accustomed to playing in the NIT, having done so more than just about any other college basketball program.

It sure is an unfamiliar feeling for North Carolina, though.

The two teams will meet Thursday night at Madison Square Garden, after a pair of semifinal victories Tuesday night that both came down to the final few seconds.

The Flyers got 22 points and five key free throws down the stretch from Chris Johnson, holding off Mississippi 68-63 in the first game. Then the Tar Heels survived everything that Rhode Island could muster in a 68-67 overtime victory that had both coaches lamenting what should have been a foul call just before the final buzzer.

It may not be the NCAA tournament, but it's still March, and there's still some madness.

"Let's be honest, that's not our goal at the start of the season, but we put ourselves here," said North Carolina coach Roy Williams, whose team can make bittersweet history by following a national championship with an NIT title.

"We put ourselves in this position because we didn't play as well as we needed to play, but then we accepted that and we tried to do the best we possibly could."

It's been good enough so far.

Injuries and inexperience combined to tarnish the Tar Heels' season early, and they didn't recover until their chances of making the NCAA tournament — and defending the title they earned by beating Michigan State last March — had disappeared entirely.

Relegated to playing in a tournament for also-rans, the Tar Heels went on the road to defeat Mississippi State and Alabama-Birmingham before knocking off a Rhode Island team that had the best RPI of any program that failed to make the NCAA tournament.

"We enjoyed playing the last Monday night last year, and you know, we play the last Thursday night this year," Williams said. "Playing the last Monday night is better, there's no question about that. But I do believe that if you're playing — if they keep playing until there's only one team standing — it's very important to be that one team."

Deon Thompson had 16 points and 13 rebounds for North Carolina, which had possession with about 5 seconds left in overtime and the shot clock about to expire when Larry Drew II forced up a shot. The rebound eventually wound up in the hands of Rhode Island's Lamonte Ulmer, who lost control as he rushed up court moments before the buzzer sounded, never betting off a shot.

Rhode Island coach Jim Baron thought Ulmer had been tripped and a foul should have been called, an opinion that Williams readily supported.

"We got the rebound and we were aiming to push it down the other end," Baron said. "I thought there was some contact and he tripped."

Dayton didn't have nearly as much controversy in the final few minutes against Ole Miss, but with Eli Manning watching on, the finish certainly didn't lack drama.

London Warren hit one of two free throws with 23.7 seconds remaining, extending Dayton's lead to two. Trevor Gaskins then drove through the lane for Ole Miss but came up short on a twisting layup, and the Flyers grabbed the rebound.

Johnson's two free throws made it 67-63 with 11.2 seconds to play, and London Warren knocked the ball out of Chris Warren's hands and out of bounds at the other end. Johnson then stole the inbound pass, got fouled and hit one of two free throws for the final margin.

"I think we showed a lot of character," Johnson said. "We know we could have easily given up, but we showed a lot of character, showing that we still wanted it and we have a chance to do something special here."

Dayton has quite the history in the tournament, making its 22nd appearance, second only to St. John's for the most of any program. The Flyers are also in the tournament's Final Four for the ninth time, but haven't won a championship since their second in 1968.

That can all change Thursday night, when Dayton plays North Carolina in a matchup that nobody could have expected early in the season.

"Some great teams have played in this," Dayton coach Brian Gregory said. "Some great teams have made it to the finals and some great teams have won the championship. It's really neat that these guys, as underclassmen and our seniors, will get an opportunity to play in the championship game and add another really nice chapter to our history."