Georgia Southern (16-10, 8-5 Sun Belt Conference) has won three of its last four games while Troy (11-14, 4-9) has lost six of its last seven.
The Eagles built a five-point halftime lead and outscored the Trojans 44-24 in the second half.
Brown, who averages 17 points, was 6 of 15 from the floor and had five of Georgia Southern's 16 steals. Crawley was 6-of-9 shooting and grabbed nine rebounds. David-Lee Jones Jr. added 11 points and Montae Glenn chipped in eight points and 10 rebounds.
The Eagles opened the second half on a 21-4 run. Brown and Glenn scored on dunks during the stretch.
No. 25 Colorado flying high, to face San Diego next
From China to the top 25.
No. 20 Washington, Tennessee go north for matchup
The No. 20 Washington Huskies hope to make a trend out of having success in unfamiliar locations when they travel to Toronto on Saturday to face Tennessee in the Naismith Hall of Fame Classic.
Oakland thinking upset ahead of visit to No. 7 Maryland
A matinee matchup in College Park, Md., on Saturday will feature the high-scoring Maryland Terrapins, ranked seventh in the nation, against the defense-minded Oakland Golden Grizzlies in a noon tip-off.