But it seemed like 60.
North Carolina led a total of 36 seconds in regulation, once at 2-0 and again in the second half by one on a Zeller layup with 10:54 left in the game, but it was Barnes who came up with big shot after big shot to truly lift the Tar Heels to the come-from-behind win.
"It was a difficult loss for us," Clemson head coach Brad Brownell said. "I thought we controlled the game in long stretches for the most part. But Harrison Barnes - we couldn't stop him and he was the difference for them. Give North Carolina some credit for bouncing back.
"They can go to a lot of options for baskets and we've seen that the last days."
The Tigers led 73-66 with 3:54 left to play, before the Tar Heels went on a 7-0 run to send it to overtime. Barnes scored on a deep three-pointer and John Henson scored on a layup before Zeller's shot capped the regulation run.
Demontez Stitt had a chance to win it in regulation with the score tied at 73, but a fall away 17 footer fell harmlessly short as time expired.
Tyler Zeller's baseline hook shot tied it at 73 shortly before that.
"We had open shots," Brownell said of the scoreless stretch. "Tanner Smith had a wide open three. (But on the last possession) We get the ball to your best player, give him space and let him make a play.
"We got the ball to our best player. We gave him space and we didn't make the shot. By the way, he got 25 points tonight so he did very well."
At that point, the Tigers were seemingly out of gas.
UNC scored the first nine points of overtime before Tanner Smith's layup pulled Clemson back within seven, breaking a scoring drought that lasted six minutes.
Having seized momentum on the strength of two three pointers, one by Barnes and the other by Kendall Marshall, the Tigers responded.
Andre Young hit a three-pointer with 10.8 left in the extra session to pull the Tigers back within three, but North Carolina hit its free throws down the stretch to seal the win.
Milton Jenning scored 16 points and grabbed 7 rebounds before fouling out in the loss. (AP)
"Growing up in North Carolina and watching them play in the ACC Championship- I wanted to beat those guys pretty bad but things didn't go our way in the end like coach said," Stitt said.
"Demontez was terrific. Played with poise and confidence," Brownell said. "He's one of the best competitors I've ever coached and we saw that today in how he competed and how he finished plays."
Clemson led by as many 14 in the first half before North Carolina closed it to 38-28 at halftime. The Tigers were hot from behind the arc early on, knocking down 5 of their first 7 attempts.
Clemson also outrebounded North Carolina 19-11 in the first half before things started to even out more in the second.
"It was unbelievable game again," North Carolina head coach said afterwards. "Clemson played well and their defense got it started. They were aggressive. They had more points on second shots, more rebounds and more fast break points - all of those are aggressive stats.
"But in the second half we got more aggressive. Harrison started making a bunch of shots. For him to get 40 points, a freshman record, he's in big time company right there."
"We lost the game because we couldn't get stops," Brownell said. "We played well enough offensively to win. The problem is we gave up 45 points in the second half. And you have to give credit to their guys- Harrison Barnes made shot after shot.
"I haven't coached against many guys who have gotten 40 against me."
North Carolina moves on to Sunday's championship game against the winner of the Virginia Tech/Duke game while the Tigers now await their NCAA Tournament destination Sunday afternoon.
Having beaten Boston College in the first round of the ACC tournament Friday, Clemson figures to be in good position to be selected for the fourth consecutive season. However the Tigers could be invited to play in the "First Four" games in Dayton, Ohio either on Tuesday or Wednesday of next week.
"I told them as we were going off the court to Brad and his team, 'good luck next week' because they should be in the NCAA Tournament," Williams said. "Those kids have accepted what Brad wants to do and that says good things about the kids but also good things about the staff."
Brownell agreed his team should be in the NCAA Tournament.
"We are playing a top 10 team on a neutral court (laughing) and we have a seven point lead with three minutes to go, if that doesn't make you good enough to the tournament I'd be shocked.
"I feel like it's unbelievable, but you better look at how teams are playing in the end. The tournament is now. Some teams haven't gotten better, they've gotten worse.
"We've know we are one of the best teams."
NOTES: Clemson is now 0-6 in overtime games at the ACC Tournament ... Barnes set a new record for scoring by a freshman with 40 points. The old record was establish by Georgia Tech's Mark Price with 33.