Chris Wilder's side took all three points thanks to John Marquis's goal on 43 minutes.
Wilder went into the game without defender Zander Diamond (ineligible) and midfielder Darren Carter (suspended). He named the following starting XI: Duke, McSweeney, Sinclair, Morris, Marquis, Hackett, Tozer, Connell, Horwood, Robertson, Ravenhill.
Virtually certain of a play-off place going into the match, Burton still had hopes of a top-three finish but manager Gary Rowett had warned his side that they would face a tough test at Sixfields.
The win leaves Northampton level on points with Wycombe Wanderers who they face on Good Friday. It also drags Bristol Rovers firmly into the relegation scrap after they lost at home to bottom club Torquay United.