Charleston Southern trailed by 11 with less than 6 minutes to play, but rallied to within three on a 3-pointer by Saah Nimley with 52 seconds remaining.
McGill then came through with his jumper that boosted the lead to five and he added two free throws with 8 seconds left to account for the final score.
Southern Mississippi (27-9) advanced to take on Louisiana Tech, which pulled off a surprising win Tuesday over Florida State.
Jonathan Mills led the Golden Eagles with 16 points and Dwayne Davis had 15. The four game-clinching points by McGill in the final seconds were his only points of the game.
Southern Mississippi finished second to Memphis in the Conference USA regular-season race and also lost to the Tigers in the finals of the league tourney.
Nimley scored 24 points for Charleston Southern (19-14).