Green, a 6-foot-2 junior, hit a 17-footer to tie the game at 53 with 1:05 left, then hit a 3-pointer with 15.5 seconds left for a 56-53 lead.
Charlotte trailed 46-32 with 12 minutes remaining, but rallied thanks to a 2-3 zone defense that limited Wright State to 22.6 percent shooting (7 of 31) in the second half. The Raiders scored on just three of their final 19 possessions.
Charlotte (6-6) won its second straight tight game after beating Tennessee 49-48 last Friday. The 49ers also got 13 points and seven rebounds from Javarris Barnett.
N'Gai Evans led Wright State (7-6) with 12 points. Cooper Land scored 10.