The Grecians went in front after 18 minutes when Arron Davies' cross was headed into the penalty area by Alan Gow and Jamie Cureton lashed a volley into the net from six yards.
Cureton turned provider for Exeter's second goal five minutes before half-time. The experienced striker did superbly to reach Liam Sercombe's cross and head the ball into the path of Davies, whose shot was too powerful for Ross Atkins in the Burton goal.
Exeter had barely got out of second gear and Burton certainly had their chances. Billy Kee's curler from the corner of the penalty area was parried wide by Artur Krysiak before the Pole made a smart stop to keep out Lee Bell's powerful drive.
Krysiak then made a brilliant instinctive stop to push Justin Richards' shot on to a post, before John O'Flynn wrapped up the points for Exeter with a fantastic third late on.
He fed the ball wide in the middle of the park before continuing his run and tapping home at the back post from Guillem Bauza's perfect cross.