The Phoenix (15-15), who won a quarterfinal game for only the third time in nine conference tournament appearances, faces Davidson in the semifinals on Sunday at 8:30 p.m.
The win avenges a six-point loss to the Eagles in January. The Phoenix shot only 35.9 percent in that game but made 53.3 percent (24 of 45) of their field goal attempts on Saturday.
Elon led by 11 points in the first half and never trailed over the final 20 minutes. Georgia Southern tied the game once, at 48-48 and was down 60-58 after a jumper by Jelani Hewitt with 2:19 left in the game. But Elon finished with five unanswered points to seal the win.
Eric Ferguson scored 21 points for the Eagles (15-15).