Chesterfield remain top of England's fourth tier on goal difference, despite failing to win for the fourth consecutive league game.
Adam McGurk's fourth and five goals of the season put Burton 2-0 ahead inside the opening quarter of an hour.
McGurk broke the deadlock on 10 minutes, finishing well in a one-on-one situation after being sent through on goal by Lee Bell's probing pass.
The lead was doubled moments later when McGurk headed home from Chris Hussey's pinpoint cross.
Burton, roared on by 612 travelling supporters, were good value for their win and could have enhanced their margin of victory further in the second half.