The Gamecocks (5-1) won their fourth straight and finished with four players in double figures. Johndre Jefferson added a season-high 11 points.
South Carolina led by as many as nine points early, but trailed 37-35 at the half because of the play of the Hornets' Marques Oliver.
The sophomore forward scored 17 of his season-high 21 points in the first half and was difficult for the Gamecocks to defend.
"What was hurting us was him driving the ball," South Carolina coach Darrin Horn said. "We made some adjustments with who was guarding him, then how were we guarding him."
But the Gamecocks opened the second half by scoring the first seven points and never trailed again. They regained the lead before Delaware State (2-3) crossed midcourt with a possession.
Jefferson was scoreless in the opening 30 minutes, but chipped in 10 points during a 15-4 run that gave the Gamecocks a 69-52 lead late in the second half.
The 6-foot-9 senior forward scored all 11 of his points in the final 10 minutes and finished one point off his career high of 12 set last year against Richmond.
"Johndre Jefferson was terrific off the bench," Horn said. "He really gave us a presence and finished well at the rim. Jefferson was the standout guy tonight."
He opened the decisive run with a jumper in the paint and later added four dunks to his spurt. He ended the run with 3:38 remaining by slamming home an alley-oop pass from Cooke.