Billet beat No. 18 Georgia Tech on Feb. 14 on a 3-pointer with 2.4 seconds left, then hit another with 16 seconds left to beat Clemson on Saturday.
"I've gotten great looks and fortunately they've been able to go down for me," Billet said. "I just wanted to give it a shot."
His shot might have also saved beleaguered UVA coach Pete Gillen's job.
"There was no doubt in his mind he was going to shoot it," Gillen said. "He didn't even look at the other guy. ... I don't want to wake up."
After the game, UNC coach Roy Williams said he was satisfied with the defense on Billet. He felt that Raymond Felton was close enough to bother the shot.
Still, Carolina had one last chance -- possession at half court with 10.1 seconds left following a lengthy delay by the officials. But the Cavs had fouls to give, and all Felton could eventually muster was a desperation three-point heave from the sideline.
When his shot fell short at the buzzer, a throng of Virginia fans stormed the court.
The Tar Heels (16-8, 6-7 ACC), which matched their biggest lead of the game at 68-59 at the 6:42 mark, failed again to hold a lead down the stretch, and in doing so, dropped their fifth straight at University Hall and slipped back into a tie for fifth place in the ACC.
Billet was just 3-for-7 from beyond the arc, but hit the big shot he has become accustomed to making in the clutch.
As time ticked down, Williams tried to shorten the game. But when a pass by May found its way into the stands, Virginia – down by one – had possession with 58.7 seconds remaining.
The Cavs (15-10, 5-9 ACC) got off two three-point attempts prior to Billet's field goal, and then retained the ball on a questionable out of bounds call, setting up his heroics.
"If we get that rebound, we win it right there," said Sean May.
On the final play of the game, UNC had hoped to give its prime time performer Rashad McCants one last look at the basket. But he never got close to the ball, as McCants managed just eight points – snapping a string of 13-straight games in double figures.
"They kept the ball out of my hands," McCants said. "They accomplished what they wanted to do. It was a prime opportunity for my teammates to step up, and they did – they kept us in the game. We shouldn't have bailed out on that [nine]-point lead. It's just something that we need to work on."
Virginia deployed a box-in-one defense on the ACC's leading scorer for most of the night.
"He wasn't patient with that," Williams added. "Then he got into foul trouble in the second half. McCants can't be all of our offense, we have to be able to play and rebound the ball."
Carolina entered the game ranked second in the ACC with a +4.2 rebounding margin, while UVa was buried in last place at –5.1. But the Cavs out-rebounded Carolina this time, 41-35.
"The bottom line is we have to rebound," Williams said. "We can't give them those opportunities."
May led the Tar Heels with 20 points and eight rebounds. Felton added 16 points, and was 4-of-7 from three-point range.
Devin Smith, who was labeled as day-to-day by his coach due to a persistent back injury, led the Cavs with 20 points and J. R. Reynolds kicked in 14 to go with Billet's 12.