Goals by Tom Flanagan, Lloyd Dyer and Tom Naylor earned three points for the Brewers, who also missed a penalty when Joe Wildsmith saved from Lucas Akins with the game goalless.
It means former Blades manager Nigel Clough remains unbeaten as a boss in nine matches.
However, it was a miserable afternoon for the Owls, who have now lost five of their last six games and have just one win in 10.
Burton could have taken a sixth-minute lead only for Wildsmith to keep out Akins’s penalty, awarded for Jacob Butterfield’s challenge on Will Miller in the area.
The Brewers went ahead eight minutes before the break when Flanagan ran unchallenged through the Wednesday defence and into the area, where he unleashed a left-footed shot into the net.
There was worse to come for the hosts when Dyer ran on to Akins’s through-ball and slotted past Wildsmith and into the centre of the goal five minutes after the break.
The scoring was rounded off a minute from time when Akins sent the ball across the face of goal where it found the oncoming Naylor, who slotted home.
Burton were handed a golden chance to go ahead thanks to Butterfield’s challenge on Miller and referee Darren England pointed to the spot.
Akins’s spot-kick was heavier on precision than power and Wildsmith guessed correctly to dive to his left to keep the ball out.
Burton were enjoying more possession and Flanagan forced the home goalkeeper to go down to his collect his header while Akins found himself in plenty of space, running into the area before sending a low shot wide.
It took the hosts half an hour to have an attempt on goal when Lucas Joao headed over Jack Hunt’s high, looping ball to the far post.
David Jones volleyed wide for the Owls from the edge of the area before Burton went ahead eight minutes before the break with Flanagan claiming his second goal in four games.
The Owls should have levelled only for Jordan Rhodes to direct his point-blank header from Adam Reach’s cross straight at Burton goalkeeper Stephen Bywater.
Half-time was greeted with a chorus of boos in Hillsborough, rising to a crescendo five minutes after the break when Dyer slotted home.
John Brayford then shot across Wildsmith before Atdhe Nuhiu’s introduction minutes later gave the hosts more shape and purpose, Rhodes’s downward header saved by the goalkeeper.
Bywater tipped Nuhiu’s half-volley round a post and Morgan Fox headed wide, but the Owls could not find the breakthrough despite dominating possession.
Instead Burton grabbed a third goal in the closing stages as Hillsborough emptied rapidly.
Sheffield Wednesday: Wildsmith, Hunt (Palmer 63), Frederico Venancio, Loovens (Pudil 46), Fox, Wallace, Butterfield (Nuhiu 52), Jones, Reach, Rhodes, Lucas Joao. Unused substitutes: Marco Matias, Baker, Dawson, Abdi.
Burton Albion: Bywater, Brayford, McFadzean, Buxton, Turner, Flanagan, Miller (Allen 71), Naylor, Murphy (Scannell 90), Dyer (Sbarra 90), Akins. Unused substitutes: Warnock, Ripley, Sordell, Akpan.
Referee: Darren England (South Yorkshire).