Stanley took the lead with their first real attack after seven minutes. Left winger Lee Molyneux's initial shot was saved by Stuart Tomlinson but he could only push it out to Will Hatfield. The striker's effort looked to have been hooked off line by Damien McCrory but the assistant referee ruled it had gone over.
Albion equalised after 36 minutes when Matt Paterson pounced on a mix-up between defender Peter Murphy and goalkeeper Paul Rachubka and he touched the ball over the line.
Padraig Amond put the hosts back in front on the hour mark when he got on the end of a long ball forward and chipped his shot over Tomlinson.
But seven minutes Lee Fowler's ball into the box was brought down by defender Zander Diamond and he stabbed home from close range.
A stunning 25-yard free-kick from Jacques Maghoma found the top of the net to put Burton ahead for the first time in the 73rd minute.
Molyneux hit the woodwork in injury-time before substitute Beattie popped up with almost the last kick of the game from close range.