Adam McGurk gave Gary Rowett's side the perfect tonic after Saturday's defeat at Scunthorpe with the only goal of a scrappy encounter.
Wycombe saw plenty of the ball, but it was Burton who had the better chances in the opening 45 minutes.
Billy Kee headed straight at goalkeeper Matt Ingram before McGurk fired carelessly high from 15 yards.
McGurk almost made amends when he hit a post with a left-footed curler in the 32nd minute.
Burton goalkeeper Rob Lainton was not tested until he had to push Nick Arnold's shot to safety shortly before the break.
The hosts went in front in the 54th minute when Kee's header left the unmarked McGurk with a simple finish from close range.
Midfielder David Gray had a chance to double Burton's lead, but fired across the face of the goal in the 70th minute.
Visiting goalkeeper Ingram did well to keep out a Robbie Weir shot in the closing stages.