Keith Treacy and Ross Wallace's second-half strikes gave the Clarets a fourth away win of the season, and provided the perfect tonic to a run of just one win in seven outings.
Burnley had the better of a turgid opening 45 minutes but were unable to make their pressure count; Sam Vokes seeing his volley deflected over the bar before full-back Kieran Trippier burst forward and rattled Chris Kirkland's bar with a 30-yard thunderbolt on 11 minutes.
Wednesday took 20 minutes to register a shot on goal - Danny Lafferty's mis-kick for Burnley allowing Jeremy Helan to feed Michail Antonio down the left. The former Reading forward's cross to the back post found Kieran Lee, and keeper Lee Grant did well to turn his diving header behind.
Burnley began to boss proceedings again and skipper Jason Shackell volleyed over from 12 yards after Danny Ings had headed down a Ross Wallace free-kick.
Wales international Vokes failed to convert Trippier's 29th-minute cross from six yards with the goal at his mercy - the ball running through the former Bournemouth man's legs when any sort of a touch would probably have sufficed.
Three minutes before the interval Brian Stock fed Vokes on the edge of Wednesday's penalty area and his reverse ball played in Chris McCann, but the midfielder fluffed his lines on his 250th appearance for the Clarets by shooting straight at the onrushing Kirkland.
The hosts could have gone ahead shortly after the break when Helan produced a brilliant run down the left and teed up Lee, whose shot was blocked by Michael Duff, the centre-half recovering to snuff out Antonio's follow-up effort.
The impressive Trippier saw one of several threatening deliveries headed wide by Vokes, before Wallace cut in from the left and forced Kirkland to tip his 30-yard effort around the post.
Treacy, on for the injured Paterson shortly before half-time, looked to have little on when he fired a hopeful low left-footed effort from 25 yards which squeezed just inside Kirkland's far post.
That sparked a reaction from the hosts, but Burnley were able to scramble Helan's low cross away.
Stock's long ball in the 65th minute found Wallace in acres of space, but the former Preston man saw Kirkland get down well to gather his effort.
Wednesday's chances of getting back into the match were dealt a major blow 15 minutes from time when Lewis Buxton handled Treacy's cross, and Wallace thumped the resulting spot-kick down the middle of the goal.
That effectively settled the contest and the closing stages petered out without incident, until deep in stoppage time substitute Marvin Bartley teed up Treacy, who rifled his effort against the post.