Albion were always the better team and completed a notable double over the Grecians thanks to second-half goals from Keith Gilroy and Shaun Harrad in the space of two minutes.
The visitors rarely looked like a team capable of regaining Football League status and have now won only once in their last six Conference games.
Burton made a bright start and as early as the third minute Paul Jones had to fingertip a Chris Hall shot over the bar.
Harrad missed a great chance to give the hosts the lead in the 11th minute when he hit the crossbar after Hall's pass had split open the visitors' defence.
The woodwork also came to Burton's rescue in the 29th minute after a free-kick by Billy Jones. The ball skidded off the head of Burton midfielder Kris Taylor and Jon Challinor put the rebound wide from close range.
The Brewers continued to dominate, however, with Harrad having a shot blocked by keeper Jones' legs.
The home team's persistence finally broke Exeter down just after the hour mark. Irishman Gilroy produced some dazzling skill as he broke onto Darren Tinson's long ball before drilling home a 10-yard shot.
Two minutes later Gilroy turned creator with a well flighted free-kick that gave Harrad the chance to punish Exeter for some loose marking with a header from five yards out.