Martin finished with 11 points and 12 rebounds for the Buccaneers (11-8, 5-2 Big South Conference), who have won three in a row. Jeremy Sexton added 12 points.
Charleston Southern won despite shooting 38.3 percent (24 of 57) from the floor for the game. The Buccaneers made up for their poor field-goal shooting by making 25 of 29 of their free throw attempts.
Kenny Mitchell's jumper gave Charleston Southern a 26-10 lead -- its largest of the game -- with 7:39 left in the first half. The Eagles (7-10, 3-4) were able to get back into the contest, cutting the lead to three points on Andre Jones' 3-pointer with 1:17 to play.
But the Buccaneers held Winthrop to one point the rest of the way to seal the victory.