Brooks made all 10 of his free throws and Sullivan all five of his for the Wildcats (10-11, 6-1 Southern Conference), who missed only once in 17 tries. Davidson shot 50.9 percent from the field, including 10 of 22 from 3-point range (45.5 percent).
Davidson led 53-25 at halftime after shooting 63 percent. The Wildcats also dominated the boards 46-26 in winning their third straight game.
Georgia Southern's Jelani Hewitt, the conference's leading scorer at 20.6 points per game, had 13 points on 5-of-17 shooting. The Eagles (9-12, 2-4), who handed the Wildcats their only conference loss last season, finished at 33.3 percent shooting and just 3 of 15 from 3-point range.
Davidson, in second place, has a home showdown with conference leader Chattanooga on Thursday.