Nimley, who made 5 of 13 3-point attempts, also had four assists. Will Saunders added 16 points and Cedrick Bowen chipped in 12.
Charleston Southern (3-1) held a 61-34 lead with 13:13 remaining in the game. Central Arkansas, which is winless in in five games, never led and trailed 28-12 midway through the first half.
The Bears, who made only 7 of 27 field goal attempts in the first half, got rolling in the second making 61.1% of their shots to outscore the Bucs 43-39 in the final 20 minutes.
Jordan Howard led Central Arkansas with 18 points, Mike Martin contributed 16 and Boo Milligan added 12.