CORAL GABLES, Fla. -- Coming off its worst loss in more than a year, No. 12 Miami needed a bounce-back win in a big way against No. 3 Virginia Monday night.

The Hurricanes got it when junior guard Davon Reed scored a career-high 21 points to help overcome a spectacular performance by Cavaliers' guard Malcolm Brogdon.

Miami moved back into sole possession of second place in the Atlantic Coast Conference race with a 64-61 victory over Virginia as the Cavaliers dropped into fourth place while losing for the second time in three games.

A senior, Brogdon matched his career high with 28 points on 12-of-18 shooting but missed a 3-point try with his team down two points and 23 seconds left in the game.

The Cavaliers (21-6, 10-5) had another chance after Hurricanes guard Ja'Quan Newton was able to convert only one of two free throw attempts to put Miami (22-5, 11-4) up 62-59 with 20.3 seconds left.

Guard London Perrantes eschewed a 3-point attempt and instead converted a layup with 4.7 seconds left. Reed then went to the free-throw line with 3.9 seconds on the clock and hit both opportunities for the final margin. Perrantes missed a desperation shot from midcourt at the buzzer.

"I thought that was just a tremendous basketball game," Miami coach Jim Larranaga said. "Two teams playing at a very high level, playing great defense, battling each other in every category."

Miami held leads of 10 points early in the second half and eight with under four minutes to play, but the Cavaliers answered the challenge each time.

After going down by 39-29 less than three minutes into the second half, the Cavaliers quickly responded with an 8-0 run and eventually worked their way to a 48-47 lead on center Mike Tobey's driving basket at the 9:36 mark.

Miami went back up 54-48, then led 60-52 following another Reed 3-pointer -- he finished with five to tie his career high -- as the teams hit the under-four-minute media timeout.

Virginia came back with seven consecutive points to make it a one-point game in the final minute.

"I thought we fought to get back in the game and we had our chances," Cavaliers coach Tony Bennett said. "I thought we left some points on the board with our finishes. We were right there and had a couple of chances.

"But the guys hit some big shots. Malcolm had a terrific second half."

Brogdon got 17 of his points and eight of his field goals over the final 20 minutes.

He had only one miss -- the 3-point attempt from the wing that could have given the Cavaliers a one-point lead in the closing seconds.

"It was decent," Brogdon said. "It wasn't great. It was off the dribble. I had to get it off quick. It was good defense. I got it off, but it didn't go in."

Miami guard Sheldon McClendon was guarding Brogdon on the play.

"He had a great game," McClendon said. "He wasn't missing."

The bounce-back win came just two days after Saturday's 25-point loss at North Carolina, the worst defeat for Miami since a 28-point drubbing by Eastern Kentucky on Dec. 19, 2014. With tipoff against Virginia just 52 hours after the final buzzer at Chapel Hill, the Hurricanes didn't have much time to dwell on the beating.

"We knew what was at stake," Reed said, "and I think we responded."

NOTES: The game went nearly eight minutes before the first media timeout, which is scheduled to come under the 16-minute mark. The first dead ball -- a foul on Virginia F Anthony Gill -- came at the 12:08 mark of the first half. ... Virginia's No. 3 ranking is its highest of the season. The Cavaliers were No. 5 for two weeks in late December and No. 4 on Jan. 4 before losing at Georgia Tech and falling to No. 13 the next week. ... Despite falling a notch to No. 12 after the loss at North Carolina, Miami has been ranked in the polls a school-record 14 consecutive weeks and in the top 15 for 11 weeks this season, also a school record. ... Virginia G London Perrantes came into the game as the ACC's top 3-point shooter at 54.2 percent. He hit just one of five from long distance Monday.