Poston made five of his seven 3-point attempts while Nelson recorded his fourth double-double.
David Efianayi added 16 points, Jamaal Robateau 12 and Laquincy Rideau 10 for Gardner-Webb (5-7), which reached 100 points for the second time this season. The Bulldogs shot 39 of 71 for 54.9 percent, including 11 of 26 from 3-point range.
The Owls (7-9), members of the United State Collegiate Athletic Association, were led by Justin Gonyea with 14 points and Danilo Radonjic with 13.
Gardner-Webb made 22 steals, seven by Rideau. The Bulldogs turned 29 Owls turnovers into 32 points and had a 52-26 advantage in the paint.
The Bulldogs shot to a 10-2 lead, led 44-25 at halftime and would go up by as many as 51 points.