To add to faltering Albion's problems, they ended the game with nine men as central defender Neil Clement and midfielder Darren Carter were both sent-off in stoppage time.
Clement faces a three-match ban after clashing heads with Leon Clarke, while Carter, who was already banned for the next two matches after collecting ten bookings, saw red for collecting two more yellow cards.
Burton's 59th minute strike earned Wednesday their seventh win in ten games and took their points tally to 24 from the last 30 to leave them in sight of the top six.
In sharp contrast, Albion's problems at The Hawthorns threaten to cost them a play-off place.
They have not won at home since beating Cardiff City back on February 20 and have now lost four of their last five league games in front of their own fans - collecting just one point from a possible 15.
They only had themselves to blame for their latest setback as they enjoyed enough possession to have won only to be undone by a neat piece of finishing by the in-form Burton.
He capitalised on a great left-wing cross from the impressive Chris Brunt, who whipped in a pinpoint centre that Burton stabbed home from close range.
Albion goalkeeper Dean Kiely was adamant that he had saved Burton's shot but television replays clearly showed the ball was over the line.
The goal sparked an Albion response but Diomansy Kamara headed wide twice and Robert Koren twice fired wide as Wednesday held on for a hard earned three points.
Albion had a sign of what was to come in the first half as they were dominant in terms of chances created in the opening period but failed to make them pay.
Carter was twice denied by goalkeeper Iain Turner, while Richard Wood blocked a goalbound drive from Kamara.
Kamara's movement was a constant danger to Wednesday and they were relieved to see him shoot into the side netting in the 24th minute.
Brunt carried Wednesday's greatest threat down the left wing, but their best chance was created by a misplaced pass from Albion central defender Sam Sodje after 29 minutes.
His back pass was intercepted by Steve MacLean but the Scotsman was unable to hit the target as Kiely narrowed the angle.
It was a rare moment of menace for Wednesday, who then had a double let off in the space of four minutes when Nathan Ellington saw his shot blocked by Lee Bullen before then firing another chance wide.