Stand-in centre back Danny Hall opened the scoring for John Sheridan's men when he controlled Derek Niven's free-kick before drilling a low effort past Brewers' keeper Artur Krysiak.
Mark Allott then fired into the bottom corner from the edge of the box after the visitors failed to clear a corner to double his side's lead.
Burton defender Aaron Webster looked to have set up a tense finish when he beat Tommy Lee from 25 yards with 11 minutes to go.
But goals from Jack Lester and Drew Talbot made the points safe before Shaun Harrad replied for the visitors in stoppage time.
And there was still time for Donal McDermott to race clear and beat Krysiak from close range.