Jeremey Hollimon scored 14 points with four 3-pointers and Wesley Person added 12 points with three 3-pointers for the Trojans (4-3), who never trailed and shot 13 of 38 from behind the 3-point arc.
John Walton III had 11 boards and Troy outrebounded Southern Mississippi 44-34.
Varnardo, who notched his fourth double-double of the season, scored four points in Troy's 13-0 opening run. The Trojans hit five straight 3s for a 31-17 lead and were up 32-21 at halftime.
Troy pulled ahead in the second half on a 13-0 run in which Person, Varnardo and Hollimon each hit 3s and led by double digits the rest of the way.