DeAndre Daniels added 17 points and tied a career high with four blocked shots for the Huskies (18-7, 8-5 Big East).
Sean Kilpatrick had 13 of his 18 points after halftime, and JaQuon Parker added 14 for Cincinnati (19-8, 7-7), which lost for the fourth time in five games.
The teams were tied a 55 before Napier hit two three-pointers as part of a 6-2 UConn run to open overtime.
A layup by Kilpatrick made it 63-60, before Napier buried his third with a minute left.
Jermaine Sanders layup cut the lead to four with 43 seconds left and the Bearcats began to foul. UConn made seven of eight free throws down the stretch.
In other games *
At Duke, Seth Curry had 22 points and the No. 6 Blue Devils (23-3, 10-3 Atlantic Coast Conference) routed Virginia Tech, 88-56.
* At Oregon, Justin Cobbs had 14 points and Cal (17-9, 9-5 Pac-12) upset No. 23 Oregon, 48-46. Carlos Emery led the Ducks 21-6, 10-4) with 13 points.
* At Arkansas, BJ Young hit a spinning layup in the lane with 6 seconds left to lift the Razorbacks (17-9, 8-5 Southeastern Conference) to a 62-60 win over Georgia.
Former North Carolina State coach Sidney Lowe apologized to family and friends after being arrested on tax charges and says he's working to resolve the issue. The state Department of Revenue says Lowe didn't file returns in 2009, 2010 and 2011.