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.
College basketball picks: Does being (or beating) No. 1 matter?
ESPN.com's college hoops experts make their picks for this weekend, which includes an intriguing UNC-Virginia matchup.
No. 2 Kansas readies for visit from No. 20 Colorado
Scrubbing all combinations involving two big men in the Kansas basketball lineup would be almost disingenuous to coach Bill Self, because the strategy contradicts presumed roster strengths.
No. 25 Utah State back home, ready for Fresno State
No. 25-ranked Utah State heads home Saturday for its first Mountain West Conference game at Dee Glen Smith Spectrum, hosting Fresno State in Logan, Utah.