Stanley's task was made easier when the visitors, who have yet to pick up a point on their travels this term, were reduced to ten men on the hour with the sending-off of Lloyd Blackman.
It took the home side just over half an hour to break the deadlock, with Leam Richardson feeding Brown, who drove home an angled shot past Cards keeper Shwan Jalal.
An entertaining encounter took a dramatic turn in favour of the Reds on the hour as Blackman was sent off after picking up a second yellow card and Craney curled home the resulting free-kick.
Mark Rawle scored a late consolation for the visitors, but it was too little too late for Glenn Cockerill's side.