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.
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