It came after 26 minutes, courtesy of a dreadful mix-up between Kelvin Langmead and Shane Cansdell-Sherriff that left Grant with a simple chance to score from eight yards.
Coleman said: "We've got the same feeling now as when we won the Conference. People will say we'll run out of steam but the lads are very confident. We're going well and it bodes well.
"They say goals change games and it came at the right time for us."
Stanley also had three penalty appeals turned down, and Coleman added: "Two of them defied belief, especially when John Miles got tripped. How you've got two men - a referee and an assistant - who can't see that, well, then they're possibly in the wrong game."
Source: Team Talk