Anthony Gill added 13 points for the Cavaliers (30-6), who turned in a dominating performance while controlling the tempo and shutting down the eighth-seeded Tigers (24-10) at nearly every turn.
Virginia led by 15 at halftime and pushed that to 27 points late, picking right up where it left off in its strong finish to Friday's tournament-opening win against Coastal Carolina.
In what has already been the program's most successful season in decades, Virginia added another milestone: its first regional semifinal appearance since making it to a regional final in 1995. And the Cavaliers, carrying a No. 1 seed for the first time since the days of Ralph Sampson, look ready to go even farther.
Now they're headed to New York to face fourth-seeded Michigan State (28-8) on Friday night in the East Regional semifinals at Madison Square Garden.
The reasons were all on display against a Memphis team eager to speed up the deliberate-paced Cavaliers and score in transition to avoid working against Virginia's stingy set defense.
Instead, Coach Tony Bennett's team checked nearly everything off its to-do list, steadily overpowering the Tigers with confident efficiency.
The Cavaliers knocked down open looks. They played tough in the paint to contest Tigers' drives. They patiently ran their offense to make Memphis defend deep into the shot clock, then snatched down every loose rebound when the Tigers missed chances to cut into the deficit.
There was no sign of the Virginia team that looked out of sorts while falling behind by 10 in the first half Friday against the 16th-seeded Chanticleers. Only the one that put Coastal Carolina away in the final nine minutes.
Harris led the offensive effort that had five players scoring in double figures. Virginia also had a 40-28 advantage on the boards while backed by a loud crowd filled with Cavs fans who made the drive one state south for the start of Virginia's tournament push.
Austin Nichols scored 15 points to lead the Tigers, who shot 41% — including 3 of 13 from 3-point range — and scored 17 points fewer than their season average.
Memphis came in looking for its first trip to the round of 16 since 2009, John Calipari's final year as coach before Josh Pastner took over. The Tigers hadn't made it out of the opening weekend since, prompting senior guard Geron Johnson to promise shortly after the American Athletic Conference tournament that this year would be different.
Instead, Memphis' season ended on the opening weekend of the NCAA tournament for the fourth straight year.