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.
Morant's triple-double leads Murray St past Marquette, 83-64
Ja Morant logged the ninth triple-double in NCAA Tournament history as Murray State trounced fifth-seeded Marquette 83-64 in the first round of the West Region.
VCU expects to have top scorer Evans in opener
VCU leading scorer Marcus Evans practiced Thursday and is expected to play in the Rams' game against UCF in the first round of the NCAA tournament.
LSU, Maryland big men set for showdown
LSU and Maryland's big men led the way in first-round victories in the NCAA East Regional. Now they'll go head to head in a second-round game Saturday in Jacksonville, Fla.