Goals from Andy Corbett and Jimmy Phillips brought them the points after Chris Jones had given Grimsby a fourth-minute lead with his first goal for the club.
Grimsby went ahead with a freak goal. There seemed no danger as keeper Artur Krysiak prepared to clear a backpass but he was closed down by Jones, who jumped in the air and saw Krysiak's clearance cannon off his back and rebound into the net.
But Burton then dominated with some fine football and deservedly levelled just six minutes later. Phillips crossed from the left Richard Walker missed his kick but the ball went through to Corbett at the far post, who swept home with his left foot.
Guy Branston headed narrowly wide from a corner before Burton went ahead on the half-hour. A sweeping move culminated in a Michael Simpson lay-off to Phillips who curled a delightful right-foot shot into the far corner.
Krysiak made up for his first-half blunder with a fine save from Grimsby substitute Danny North after 56 minutes. North was one-on-one but Krysiak raced out to block his shot fellow substitute Peter Bore was also denied by the keeper, Krysiak holding his fierce shot at the second attempt.