Napier shot 9-of-10 from the free throw line and grabbed a team-high six rebounds in the win. Ryan Boatright netted 16 points while Lasan Kromah came off the bench and provided a ton of energy en route to 14 points and four steals.
Connecticut (10-1) was coming off its first loss of the season, a 53-51 heartbreaker to Stanford.
C.J. Wilcox scored 19 points for Washington (6-5), which had its brief two- game winning streak come to an end. Wilcox, who surpassed 1,500 career points last time out, passed Louis Nelson and Steve Hawes for ninth place on UW's all-time scoring list.
Darin Johnson chipped in 13 points off the bench and Mike Anderson tallied 10 with eight rebounds.
Washington assumed control early on, jumping out to a 31-17 edge on Wilcox's triple at 7:03 of the first half. UConn then came alive, using a 15-2 surge to pull within a point. After Anderson ended the run, Boatright drilled a 3- pointer to tie it at 35-35.
Napier's first bucket of the game came seconds before the halftime buzzer and put the visitors in front 43-39 at intermission.
Napier picked up where he left off in the second period, sinking his first two jumpers to extend the margin. Kromah capped a 6-0 burst with a jumper of his own for a 10-point edge, but Washington responded and pulled to within 53-48 on consecutive treys by Johnson and Wilcox.
Then, Washington went cold. The Huskies went more than four minutes without a basket as Connecticut built a 62-48 lead.
"We had the opportunity to put our foot on them, but we let them go," said Wilcox. "I think it was mostly us. We had a lot of unforced turnovers."
The two teams played even the rest of the way, with Washington getting as close as eight points with 8:27 to play. But UConn turned it up defensively down the stretch, forcing 11 seconds half turnovers as it rolled to the finish line.
DeAndre Daniels scored 10 points for UConn ... Washington fell to 6-6 at home against top-10 foes under Lorenzo Romar ... Connecticut shot 54.9 percent from the floor and 88 percent (22-of-25) from the free throw line.