Burton showed why they have a good record on the road when they stunned the home fans with two goals in the space of five first-half minutes.
Chris Hussey had already shot against the Chesterfield bar before Lee Bell sent McGurk clear of a static defence in the 10th minute to place a low shot past Tommy Lee from 12 yards.
McGurk struck again in the 14th minute when another quick Burton counter ended with Hussey crossing from the right for the striker to steer a header inside Lee's right-hand post.
Robbie Weir should have made it three but missed an open goal from close range in the 24th minute and Lee had to save from McGurk six minutes into the second half.
Armand Gnanduillet headed a free kick wide but Burton wasted another chance in the 64th minute when Jimmy Phillips side-footed wide after Lee parried a Matty Palmer free kick.
Jordan Pickford made late saves from Jay O'Shea and Gnanduillet but Burton were comfortable winners.