Having seen fellow title-chasers Hereford United reduce the gap to 13 points at the top of the table, Stanley quickly re-established their 16-point lead with their rivals not in action.
Stanley are now unbeaten in 16 matches, bettering Grays Athletic's 15-game unbeaten record when they led the division earlier in the season.
Nigel Clough's Brewers made life difficult for the home side, and went into the match with plenty of confidence having lost just three of their last 17 matches.
But Paul Mullin's ninth-minute goal was the perfect platform for Stanley to stamp their authority early in the action. They didn't look back.
Experienced hitman Mullin headed home after the visitors had the better of the play in the opening exchanges.
Andrew Corbett had a shot saved by Stanley goalkeeper Robert Elliot in the seventh minute, and a minute later Jon Shaw forced Elliot to save his powerful header.
But up popped Mullin just when Stanley needed him most. His pin-point header was his 152nd goal for the club and his 12th of the season.
The striker celebrates his 32nd birthday next month and, if Stanley do get promoted (which looks a certainty now), then League Two football should beckon for the experienced striker.
Mullin's goal spurred Stanley on and Ian Craney nearly doubled the home side's advantage, but his shot flew over.
Then it was all Burton for the remainder of the half. Shaw fired over in the 27th minute and Chris Hall saw a shot saved.
Shaw fired wide in the 38th minute, before Romauld Boco had a shot charged down for Stanley.
Andrew Ducros shot wide as Burton piled on the pressure and on the stroke of half-time Shaw equalised with a clinical strike.
The re-start saw Hall have a shot blocked, while Kris Taylor had three excellent chances, all of which went begging.
In the 56th minute he failed to hit the target, fired over in the 68th minute and then had a shot saved by Elliot two minutes later as Clough's men failed to make Stanley pay.
Craney went close for Accrington as they tried to get a foothold on proceedings, but Burton just kept on pressing.
Shaun Harrad forced Elliot to save well in the 74th minute, before Terry Henshaw also had an effort saved.
But despite dominating the visitors hit with a sucker-punch when Robbie Williams netted a cruel winner in the dying seconds.
Goalscorer Mullin met a Gary Roberts corner and headed goalwards. Burton failed to clear their lines and Williams fired home from close-range to secure three welcome points.