Striker Billy Kee celebrated his return to the starting line-up in place of injured top scorer Calvin Zola with two clinical finishes in the 36th and 55th minutes.
The Brewers were a goal up when David Noble picked up his second yellow card on the stroke of half-time and after Kee's second Michael O'Connor saw red after bringing down Jacques Maghoma in the area.
But the visitors were spared a heavier defeat when Michael Symes' spot kick was saved by Andy Warrington.
The Burton boss said: "It was a brilliant result and I'm very proud of the lads.
"It's been an horrendous week in terms of preparation because apart from those who didn't play, we had four others who haven't trained and could have broken down at any minute.
"We knew that everyone would have to play their part because we knew it would be a competitive and aggressive game.
"I think you could argue that we had a little bit of fortune with the first sending off, but I think we earned that fortune with the hard work, the energy and the commitment that we showed.
"There were some immense performances out there and to preserve out wonderful home record was an absolutely monumental achievement.
"I think we've created a side that on its day is more than a match for any of the big guns in this division."