The Eagles (8-6, 2-0 Big South) shot 51.7 percent from the field and drilled 15 of 28 from beyond the arc. Moore, Smith and Christian Farmer each sank five 3-pointers apiece.
After leading 42-38 at halftime, Winthrop pulled ahead as Moore hit two 3-pointers to fuel a 12-2 run.
Charleston Southern (7-8, 1-1) fired right back as Matt Kennedy converted a three-point play to ignite a quick 11-0 run. The Eagles rolled from there as Farmer hit a trio of 3-pointers to push their lead back to double digits for good.
Winthrop led by as much as 22 and scored 28 points off turnovers. Farmer finished with 15 points and Larry Brown added 11 with eight rebounds.