Napier finished with 20 points, going 9-of-10 from the free throw line and hauling down six rebounds for UConn (10-1), which bounced back from a 53-51 loss to Stanford.
Ryan Boatright scored 16 points and Lasan Kromah added 14 with five steals off the bench.
C.J. Wilcox paced Washington (6-5) with 19 points.
Darin Johnson scored 13 points and Mike Anderson had 10 points and seven rebounds.