Burton suffered their second home loss of the week after defeat by Accrington.
Stanley, who are gaining on Albion in League Two, took the lead through Kevin McIntyre's deflected 25-yard free-kick.
Burton were denied an equaliser when Ian Dunbavin saved Justin Richards' volley from point-blank range.
After the break Stanley's Padraig Amond sent Luke Joyce's cross wide but their lead was doubled when Ryan Austin headed Craig Lindfield's corner into his own net.
VIEWS FROM THE DRESSING ROOM
Burton Albion manager Paul Peschisolido told BBC Radio Derby:
"Calamity - you set up a wall up and the ball goes through it. One shot on goal, 1-0 down. In the second half, again they didn't have anything apart from a corner kick set-piece. Ryan was the wrong side of his man and headed it in. To be honest, I need to see it again, but it looked like a calamity of errors.
"I'm disappointed with that. It's another two goals at home, another two goals against and it looks like the goals have dried up at the other end, which I'm concerned about too.
"I'm looking for people to try and make things happen. I've given them the freedom to play, but too many players were negative today. They were scared to get the ball and they were scared to make things happen."