The lead changed hands five times early - and was tied twice - before Davenport and Beau Beech scored baskets and Aaron Bodager added a 3-pointer, and North Florida (9-4) opened a 16-10 lead after the 7-0 run. The lead grew to 41-24 by halftime.
Chris Horton scored the last six points of the game - including back-to-back dunks - as Austin Peay (4-7) cut the gap in the final minutes. Horton scored a career-high 28 points on 13-for-19 shooting to lead the Governors, the only one in double figures, and added 17 rebounds.
North Florida made 31 of 63 shots (49 percent) and made 13 3-pointers - the seventh straight game with 10 or more 3s.
Beech scored 14 points and Dallas Moore 12 with eight assists for the Ospreys.