The Tigers (31-5) advanced in the NCAA tournament for the first time in Josh Pastner's four seasons. The Conference USA champions are headed home because they struggled to stop Harris on the outside or his teammates inside all afternoon.
The Spartans' top post players Adreian Payne and Derrick Nix combined for 27 points and 18 rebounds.
Memphis' Geron Johnson scored 13 of his 16 points in the first half, and Joe Jackson finished with 12 points.
Michigan State led by as much as 13 in the first half, creating that cushion when Harris made his fifth shot and fourth 3-pointer with 7:59 left in the first half.
Memphis responded with a 12-2 run to pull within three, and the Spartans led 32-29 at halftime.
But the Tigers fell off the pace in the second half because they were overmatched physically by a Big Ten power after going undefeated during their regular season in Conference USA.
Harris got into foul trouble early in the second half, getting called for his third and fourth fouls, sending him to the bench with 13:42 left.
Keith Appling picked up the slack by making his first shot to put Michigan State up by nine points, but the team's leading scorer left for good with 8:35 left when his right shoulder took the brunt of Johnson's drive into the lane.
Before Appling was hurt, he had a towel thrown at him during a heated exchange by Nix, his teammate since high school. Izzo, who has lamented the team's lack of leadership all season, looked dumbfounded at Nix, upset that the senior center would lose his cool at a time like that.
Backup point guard Travis Trice had four fouls, limiting his ability to fill in for Appling, and that put the ball in the hands of freshman Denzel Valentine.
But it didn't really matter who was on the court for the Spartans because they were able to force Memphis into a half-court game and it struggled to have success against Michigan State's in-your-face defense.
Michigan State limited the Tigers to sub-30-percent shooting and outrebounded them by 20, a part of the game Pastner was worried about for good reason.
Izzo has built his program on defense and rebounding, and it has served the 2000 national championship coach very well. Michigan State is two wins away from its seventh Final Four under Izzo.
The Spartans and rival Michigan, which routed VCU earlier in the day in the same sold-out arena near their campuses, are in the same round of 16 for the first time.
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