The victory was the sixth in a row for the Cavaliers (7-2) and came after they limited the Vols to 28.8 percent shooting and just 15 field goals.
Trae Golden scored 11 to lead Tennessee (4-3), which scored just 36 points in a one-point loss to No. 15 Georgetown on Friday and picked up where it left off.
The Vols scored just six points in the first 14:50 of the game, and just five more after using a 12-2 run to get within 38-33 with 7:41 left. Golden and Skylar McRae hit 3-pointers in the burst, and Kenny Hall closed it with two free throws, but Tennessee scored just one point over the next 6:14.
The Cavaliers, meantime, became the fourth team held scoreless for a period of six minutes or more by the Vols this season, and with the drought at 6:18, Virginia coach Tony Bennett called timeout. After the break, Harris fed Mitchell down low for a short bank that pushed the Cavaliers' lead back to 40-33.
A free-throw by Jarnell Stokes for Tennessee made it a two-possession game with 3:03 left, but Harris scored inside for Virginia, and neither team scored again until Jordan McRae's dunk for the Vols with 1:27 to play. After Harris missed the front end of a one-and-one for the Cavaliers, Stokes' putback made it 42-38 until the Vols fouled freshman guard Teven Jones, who made both halves of a one-and-one.
The Vols scored the first five points after halftime to pull within 25-21, but consecutive layups by Jontel Evans, Virginia's first 3-pointer of the night from Harris and Mitchell's putback restored the margin to 34-21. The Cavs added two more on an inbounds play when the Vols lost track of Harris and Evans fed him right in front of the basket for an uncontested layin, making it 36-21.
Virginia led 25-16 at halftime, and that was after the Vols outscored them 10-4 over the final 5:10.
Mitchell had seven of his nine first-half points during a 19-4 burst that took more than 10 minutes and gave Virginia a 21-6 lead. Three dunks by Kenny Hall sparked the Vols run to close the half.
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Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.