Napier made four 3-pointers, including a late 4-point play, and also had seven assists and three steals for the defending national champion Huskies (5-0). Connecticut shot 52 percent (25 of 47) from the field and 40.9 percent (9 of 22) from 3-point range to easily overcome 19 turnovers.
"Overall, a win is a win, but no one's played us even near that hard since we played Butler last year," said UConn coach Jim Calhoun, whose team beat Butler in the NCAA title game last season.
The Huskies will face Central Florida in the second round. UCF beat College of Charleston 74-63.
Matt Dickey led Asheville (2-3) with 18 points, and Jeremy Atkinson added 18.