Napier, the East Regional's most outstanding player, hit three huge free throws with 37.6 seconds left at Madison Square Garden to carry UConn to the Final Four just as Kemba Walker did in Napier's freshman year.
The Huskies (30-8) rallied from a nine-point second-half deficit to become the first No. 7 seed to reach the Final Four since the tournament expanded to 64 teams in 1985.
Fourth-seeded Michigan State's seniors become the first four-year players recruited by Tom Izzo to fail to reach the Final Four. Gary Harris led the Spartans (29-9) with 22 points.
The undersized Huskies matched Michigan State's physical play box-out for box-out, holding the Spartans to just six offensive rebounds and six points in the paint. UConn dared Michigan State to shoot 3-pointers, and the Spartans nearly made enough, going 11 for 29 from behind the arc.
Trailing 51-49 with more than two minutes left, Michigan State had a chance to tie or take the lead. But Adreian Payne fumbled the ball away, and Napier drilled a jumper on the other end.
After Payne hit a pair of free throws to pull the Spartans back within two, Keith Appling was called for a foul on Napier's 3-point attempt. The senior extended the lead to 56-51, and after Travis Trice missed a 3, Michigan State couldn't get to UConn to foul. Phillip Nolan slipped free for a dunk that clinched the victory and had thousands of Huskies fans in the Garden leaping up and down.
UConn won its third national title in 2011, but the Huskies were ineligible for last year's tournament because of previous low scores on the NCAA's academic progress measure.
Ryan Boatright made four steals as UConn used its quickness to force 16 turnovers. DeAndre Daniels shut down Branden Dawson, who scored 24 points in Michigan State's Sweet 16 win over top-seeded Virginia. Dawson attempted just three field goals, making one, to finish with five points.
The 6-foot-10, 245-pound Payne hit two long jumpers to put Michigan State up 32-23 less than four minutes into the second half. But Napier started driving, getting the bigger Appling in foul trouble and UConn back in the game.
After hitting four straight free throws to tie the score at 32 with 12:38 left, Napier was struck in the face by Gary Harris - the UConn guard was called for a foul on the play - and left the court with his nose gushing blood. He was back less than minute later when Daniels completed a three-point play to give the Huskies the lead for good.
Boatright hit a contested 3-pointer with the shot clock winding down to put UConn up 49-39 with less than seven minutes left. But the Spartans rallied behind their long-range shooting.
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