Burnell had 19 points and 13 rebounds for the Gamecocks (15-6, 7-1), who bounced back from their first Ohio Valley Conference loss at Eastern Kentucky.
The game was tight all the way. The Gamecocks got some breathing room when Burnell's jumper capped a 6-0 run that made it 67-62 with 5:40 to go and Mostella's layup turned that into a 10-2 surge for a 71-64 lead at the 4:34 mark.
The Eagles (8-13, 4-4), who had won four straight, made three straight free throws but Mostella hit a jumper and Burnell had a tip-in that made it 75-67 with 2:21 to go. That was the biggest lead for either team.
Morehead got it down to four at 1:27 but the Eagles had to foul three times to force the Gamecocks to the line, and after Burnell made two free throws with :28 to go they missed two 3-point attempts.
No. 25 Colorado flying high, to face San Diego next
From China to the top 25.
No. 20 Washington, Tennessee go north for matchup
The No. 20 Washington Huskies hope to make a trend out of having success in unfamiliar locations when they travel to Toronto on Saturday to face Tennessee in the Naismith Hall of Fame Classic.
Oakland thinking upset ahead of visit to No. 7 Maryland
A matinee matchup in College Park, Md., on Saturday will feature the high-scoring Maryland Terrapins, ranked seventh in the nation, against the defense-minded Oakland Golden Grizzlies in a noon tip-off.