NEW YORK — North Carolina wanted to extend its season for one more game. To do so, it had to extend it another five minutes, first.

The Tar Heels (20-16) needed overtime Tuesday night to beat Rhode Island 68-67 at Madison Square Garden in the semi-finals of the National Invitation Tournament. But thanks to some more late game (regulation) heroics by point guard Larry Drew II, and and an extra-period scramble down the stretch, they will play Dayton in the title game at 7 p.m. on Thursday.

“One of the players said in the locker room, sometimes to helps to win ugly – and we did win ugly today,’’ said UNC coach Roy Williams.

UNC was trailing 59-54 with 1:29 left in regulation, when Drew (who buried the game-winner in the second round at Mississippi State) scored his team’s final five points – on a jumper, a free throw, and a drive to the basket – to knot the score 59-59 with 55 seconds left.

After Ram Delroy James missed two free throws with 26.9 seconds left (URI missed 5 of its final 6 foul shots in regulation, including the front ends of two one-and-ones), the game went to the five-minute extra period when Drew’s long jumper was partially blocked.

Two Deon Thompson free throws with 2:15 left in overtime gave UNC a 68-65 lead. Cothran’s shot off the glass cut it to 68-67. But with about 42 seconds left, after Drew and Thompson both missed shots, UNC got a fresh shot clock when the ball appeared to go out of bounds off a URI player.

With 4 seconds left, Drew missed a jumper, the ball got tipped out, Ram Lamonte Ulmer briefly came up with it – but UNC junior Will Graves inadvertently tripped Ulmer when he was trying to dive for the ball. Ulmer coughed it up, and it ended up in the hands of Drew.

"I was just trying to get to it any way possible, and not let them get another shot off,'' Graves said of the play. "I tried to dive on the floor for the ball when it was rolling, do whatever any Carolina player would do."

Asked if there was any contact with the URI player when he was diving on the floor, he said: "no comment."

At times, it didn’t look like UNC might have a chance to be in a game-winning situation, though, what with its poor shooting (34.9 percent) and 17 turnovers.

After Thompson scored to give his team a 25-19 lead with 8:20 left in the first half, UNC managed only two more field goals – one from sophomore Tyler Zeller, and another from Thompson on a three-point play that knotted the score at 30-30.

UNC turned the ball over six times during that time period, missed four free throws and multiple layups and putbacks. Both teams were shooting 31 percent at the break.

Trailing 46-44 with about 10 minutes left in regulation, the Tar Heels started pulling away, briefly when Dexter Strickland scored on back-to-back layups, Thompson scored on an inside move, and – after freshman John Henson missed a dunk off the back of the rim – Thompson buried a free throw to make it 51-46 with 7:59 left.

But URI countered that 7-0 run with an 8-0 comeback, taking back a 54-51 lead on an alley-oop dunk Ulmer.

Thompson led the Tar Heels with 16 points and 13 rebounds; junior Will Graves added 14 points and Drew had 9 points and 5 assists.

Cothran led URI with 23 points.

robbi.pickeral@newsobserver.com or 919-829-8944