CHAPEL HILL For Duke, 20 wins. For North Carolina, 20 woes.

That was the story Wednesday night from the Tar Heels' Smith Center, often referred to as the Dean Dome. It was more like the Doom Dome this cold winter night.

During a game when the No. 8-ranked Blue Devils (20-4 overall, 8-2 ACC) played some of their least-effective offense of the season, Carolina (13-11, 2-7) finally found some energy but hardly enough execution to make the most of the opportunity. The Heels could only watch and wish as Duke pulled away late for a 64-54 win.

The upshot is that UNC and N.C. State (14-11 and 2-8 in the league after a 20-point Wednesday loss to Virginia Tech in Raleigh), will play here Saturday afternoon in a basketball version of a futility bowl. The loser will have last place in the conference to itself.

Duke, favored by six points by game time, snapped a three-game losing streak in the celebrated series. But this win came only after senior forward Lance Thomas missed most of the second half with a knee injury and his teammates missed enough shots to help keep the Heels close until the final few minutes.

With Carolina fans hoping for an upset win that would shake their team free of its funk, the Heels led with about 11 minutes left and were tied with about seven minutes to go.

"But there are no moral victories," Carolina coach Roy Williams said. "For about 30 minutes, I thought we had the intensity we should have had all season. But they just seemed to be more hungry after that."

Williams said earlier in the week that he had never had to coach effort - only execution - but this team is an exception.

"Our personnel may not fit playing as fast as I'd like to play," he said. "But I've got to be able to do something to get them to play harder."

There was improvement on the effort front Wednesday, but not enough to match Duke over 40 minutes. The Devils worked overtime on their offensive board. Even with Thomas sidelined for the final 17:20, Mike Krzyzewski's team continually capitalized on second chances and finished with 23 offensive rebounds. Carolina had 14 offensive rebounds but did block12 shots.

"Buckets were tough to come by," Krzyzewski said. "I was proud of our team. We shot about 50 percent from three and about 20 percent from two. It was a gritty game. I know we're not a great team, but we have heart. That's how you get better. We're just not a dominant basketball team."

Jon Scheyer and Kyle Singler each went the distance and combined for 43 points. The Devils' third prong, Nolan Smith, didn't scratch in the first half but got 10 in the second.

But the possibility that Thomas may have to miss some time with the injury is a problem Duke hardly needs. Although he doesn't score much and often seems to get lost in the offense, the Devils do depend on his rebounding and defensive range.

Carolina, meanwhile, is just hurting all over. There's no obvious remedy, either. The team's flaws are so numerous that it's impossible to point to any one area as the primary problem. Team leader Marcus Ginyard said after Sunday's 92-71 loss at Maryland that the situation is "about as disappointing as it gets."

Maybe so, but there are seven games left in regular season and the Heels will not be a lock to win in a one. The Devils are probably on their way to a first-place league finish while Carolina is flirting with dead last.