Napier is among three UConn seniors who were part of the Huskies' 2011 title. That trio stayed after coach Jim Calhoun's retirement even when the Huskies were ineligible for the NCAA tournament last season.
They came back strong in coach Kevin Ollie's second season, and the Huskies (32-8) went all the way to their fourth overall title.
Kentucky (29-11), with five freshmen starters, never led in the championship game.
The Wildcats missed 11 of 24 free throws, while the Huskies were perfect on 10 tries.