Phil Edwards headed the only goal of the game a minute from time in a match of few clear cut chances.
The first half was a largely turgid affair with few opportunities. Exeter had the best of those when Alan Gow put John O'Flynn through on goal, but his finish was poor and straight at Jordan Pickford.
Billy Kee looked lively for Burton and shot just high from 25 yards before a similar long range effort was scrambled round the post by Exeter goalkeeper Artur Krysiak.
Exeter stepped up a gear after the break and again created a one-on-one chance, but Pickford was off his line quickly to thwart Gow, whose first touch was poor.
And it proved to be costly as Exeter conceded a needless corner in the 89th minute and Edwards rose at the near post to head the winner and maintain the Brewers' excellent away record.
The win lifts Burton into the play-off positions, while a second home defeat in a row for Exeter sees them drop out of the top three.