De'Andre Hunter also had 20 points for Virginia and Ty Jerome added 15 points and 11 assists.
Howard, averaging 16.5 points and 6.8 rebounds, scored 20-plus for the eighth time this season while becoming just the fourth United Kingdom player to reach 400 points in her freshman season.
During a timeout with 11:32 to play, Bennett got so heated toward his players about the turnovers that he said he "almost blew out a couple veins in my neck".
Jay Huff's layup with 3:12 remaining gave the Cavs a two-point lead, which was followed by back-to-back 3s from Guy to essentially ice the game. "The blue-collar mentality and the chip on our shoulder really makes it easy for us to make those big shots".More news: Pregnant Jessica Simpson jokes about broken toilet seat in photo
UVA junior guard Kyle Guy hit a 3-pointer with 1:10 left to give the Cavaliers a six point lead and the game.
Clark played outstanding defense on North Carolina standout freshman guard Coby White, forcing two turnovers on a 10-0 Virginia run that saw the Cavaliers run out to a 18-11 lead with 12:41 left to play in the half.
The game was closer than that throughout much of the night - UNC took the lead in the second half and was threatening to win, leading by seven points with 8:58 to go - but Virginia made stops and big shots down the stretch. His 11 field goals - which included seven 3-pointers - were the most by a UNC player in a game this year.
"There's no excuses", said Jerome, who had 15 points and 11 assists. And the Cavaliers were committing so many turnovers that coach Tony Bennett's frustration bubbled over in the huddle. He made two in the last two minutes and they were significant. The teams traded baskets for the three minutes until the Cavaliers pulled away for good.
The miracle shot, which came about because the freshman point guard lost track of time at the end of a possession, was originally ruled to be good. He hoisted a desperate 3-pointer and appeared to score, but the shot was negated after an official review revealed he didn't let go of it before the shot clock expired.More news: Horse racing in Britain to resume Wednesday -BHA
Guy and Hunter led both teams in scoring with 20 apiece.
"I just keep shooting it, because when Ty and 'Dre and guys like that have confidence in me, it's hard not to keep shooting", says Guy. "That's something I've worked for". He chose to skip the pregame shootaround at the Dean E. Smith Center on Monday. UNC went ice-cold shooting in the final minute and couldn't recover. We had a great run. and after that, it got a lot more hard.
Before he got hot in the closing nine minutes, Guy had misfired on five of his previous six shots from the floor.
True to form, UNC dominated in the rebounding category, posting a 38-27 overall advantage and 16-3 cushion in offensive rebounds.
Just when it seemed as though No. 8 UNC might be ready to take over, No. 4 UVa. slammed on the brakes of both the Tar Heels' momentum and their seven-game winning streak. The Cavaliers were able to hold the fast-paced UNC offense to just 6 fast break points.More news: North Atlantic Treaty Organisation won't station more nuclear missiles in Europe despite threat from Russian Federation
"We've got a lot of cold-blooded guys on this team", Guy said. "Every game we come out and we expect to win.' No matter where we are, and no matter who we're playing against".