Joe Harris had 16 points and five rebounds and the Cavaliers routed Memphis, 78-60, to advance to the Sweet 16 for the first time since 1995.
Virginia (30-6), which is a No. 1 seed for the first time since 1983, tied a single-season record for victories with the triumph.
The Cavs survived a scare from 16th-seeded Coastal Carolina in the second round. The contest was tied 47-47 with under nine minutes left before they embarked on an 18-5 run that finally put the game away.