Ian Craney headed the hosts in front after 10 minutes but Ryan Hall levelled matters in the 58th minute.
Terry Gornell restored Stanley's advantage in the 80th minute before Phil Edwards wrapped up the points from the penalty spot six minutes from time following Bilel Mohsni's rash challenge on Gornell, for which he was dismissed for a second booking.
Coleman said: "I think we were the better team. They are a good team and caused us a few problems but we have worked on our set-pieces a lot and it has paid off.
"I think we deserved the win for the chances we created in the game. The lads have shown a lot of character as they had a kick in the teeth when they were not paid. They have taken it in their stride. They have had a lot to deal with in the last six months while the ownership issue has been going on and I cannot thank them enough.
"They have not sulked but have gone out and given their all and a lot of the higher-paid players could take an example from this team. They have families to feed and mortgages to pay but they have shown a great appetite and professionalism."