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.
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Wesley Harris scored a career-high 27 points as Tennessee State defeated Chicago State 80-74 on Friday.
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Florida will name its basketball court after former coach Billy Donovan, who led the Gators to two national championships and four Final Four appearances during his 19 seasons in Gainesville.
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ESPN.com's college hoops experts make their picks for this weekend, which includes an intriguing UNC-Virginia matchup.