Jace Hogan added 13 points and Tim Abruzzo 11 for the Midshipmen (11-5, 2-1 Patriot), who shot 54 percent and made 21 of 26 free throws. Kelly also blocked two shots to tie for third at 151 on Navy's all-time list.
The victory was the first by Navy over BU with the series at 6-1. The Midshipmen are off to their best start since opening 11-4 in 2008-09.
Dunbar gave Navy the lead for good with a basket with eight minutes left. The lead hit 13 points after four free throws by Abruzzo with 1:10 to go after flagrant and technical fouls were called on Eric Johnson.