Ryan Arcidiacono scored 18 points to pace four Wildcats in double figures. James Bell wrapped up his Villanova career with 14 points before fouling out with 33.7 seconds to play.
What was worse for the Wildcats was that the Huskies (28-8), who will now play the winner of Sunday's Iowa State-North Carolina game in the East Regional semifinals Friday at Madison Square Garden, outplayed them in the first half while Napier was on the bench with two personal fouls.
Napier left the game with 12 minutes, 9 seconds to play, and Darrun Hilliard then hit a three-pointer to give Villanova its largest lead at 19-9. But the Wildcats then missed their next 10 field-goal attempts and were outscored, 16-1, by the Huskies over the next 10 minutes to fall behind by 25-20.
Villanova trailed by only 25-24 at the half after a free throw and Arcidiacono's three. But it failed to take advantage with Napier absent, and the senior all-American candidate then went on to score 21 points in the second half.
"It's disappointing," Wildcats coach Jay Wright said of how the Wildcats played in the first half. "In a game like that, you've got to take advantage of something like that, which we didn't. But even though we were pretty poor offensively, we still were down one, and we felt like we were in good shape at halftime."
He said UConn guards Ryan Boatright and Terrence Samuel, who played in Napier's place, "did a pretty good job of covering up and getting them back in the game."
The Wildcats took their final lead, 36-35, on the second of back-to-back three-pointers by Bell with 15:35 remaining. But Villanova managed just one field goal - another Bell three-ball - over the next 111/2 minutes.
The Huskies regained the lead with the help of a 16-4 run that ended with Napier's trey with 8:59 remaining, giving UConn a 51-40 advantage. The Wildcats closed to within five points at 56-51 on JayVaughn Pinkston's layup with just under four minutes to play, but UConn spurted again to open up a 63-53 lead on Napier's free throw with 1:45 remaining.
The Wildcats went on a furious run from that point, getting as close as 68-63 on Kris Jenkins' three-pointer with 58.3 seconds to play. But the Huskies hit 9 of 10 free throws from that point to ice it.
Napier, who sat out the last 12 minutes of the first half in foul trouble, scored 21 of his 25 points in the second half, including four three-point baskets.