Jack Lester scored twice and Marc Richards netted his debut goal for Chesterfield but Accrington hit back with a brace from Rommy Boco and a close range finish from Peter Murphy before Forbes won it.
Charlie Barnett hit the Chesterfield bar in the sixth minute, but within five minutes they were chasing the game after the home side scored twice. A back header by Accrington skipper Luke Joyce let Jack Lester in to brilliantly lob keeper Ian Dunbavin from 18 yards in the eighth minute and Richards headed in Lester's cross three minutes later.
But the visitors were back in it in before the half hour after Barnett crossed from the right for Boco to head in and they deservedly equalised
in the 58th minute when Murphy stabbed in a cross at the back post.
Accrington went behind again in the 66th minute when a cross from the right was allowed to reach Lester, who scored from eight yards but 10 minutes later Boco drilled in an 18 yard shot to level.
Defender Michael Liddle was sent off for going through Lester in the 83rd minute and a minute later, the striker crossed for Forbes to smash in the winner from 10 yards.