McRae scored 21 points, while Josh Richardson and Jarnell Stokes each added 20 points for the Volunteers (8-4).
Tennessee scored first and never trailed. The Cavaliers (9-4) left the hot-handed Richardson open in front of their bench, and Richardson cleanly sank a 3 that gave the Vols a 27-11 lead with 10:53 remaining in the first half and control of the game.
A Tennessee team that has been sluggish on offense in recent games couldn't miss. The Vols shot 57.7 percent from the field and 8-for-11 from 3 in the first half, including a buzzer-beating half court shot by Antonio Barton that gave them a 48-26 halftime lead.
Tennessee managed to keep Virginia off-balance on offense. The Cavs shot just 32.1 percent for the first half.
Mike Tobey added 10 points for the Cavaliers.
Virginia scored the first two baskets after halftime, but it was as close as the Cavaliers would get-the game was too far out of reach.
It was a far cry from last year's meeting between the two teams in Charlottesville. Virginia held the Vols to their third-lowest point total since the 1985 introduction of the shot clock en route to a 46-38 win on Dec. 5, 2012. Tennessee surpassed that point total with a 3-pointer by Barton with 4:36 left in the first half that made it 39-15.
Both teams reached the NIT last season and had set their expectations for the 2013-14 season higher with NCAA tournament hopes. Instead, they've both stumbled through the first half of the season.
Tennessee entered the game having won just six of its first 10 to continue its recent history of sluggish starts. Virginia posted consecutive losses at home to No. 4 Wisconsin - ranked eighth at the time - and at Green Bay before bouncing back with victories over Northern Iowa and Norfolk State in its last two games.
The victory was an especially important NCAA resume-building win for the Vols, who face a weaker conference lineup.