An untidy first half saw Brian Laws' outfit having little difficulty in containing a clueless Palace side and they only had to wait 12 minutes after the break to go in front through Deon Burton.
Although Clinton Morrison levelled for Palace on 80 minutes, Marcus Tudgay restored Wednesday's lead to secure their eighth away win of the season.
On a fine afternoon offering perfect playing conditions and in front of Palace's largest crowd of the season, the match was poor value.
Steven MacLean had a couple of opportunities in the first half but Gabor Kiraly came to Palace's rescue with fine stops.
At the other end, Morrison had a useful chance or two but his efforts were driven straight into the arms of Iain Turner.
The deadlock was broken on 57 minutes with Wednesday deservedly going in front.
Chris Brunt made ground down the left byline before crossing for Burton, who was well placed to nudge his header wide of Kiraly.
The Owls were enjoying their best spell and Burton missed two easy chances that would have wrapped up the points for the Yorkshire side.
But Morrison levelled with ten minutes remaining with a far post header from Mark Kennedy's in-swinging free-kick after Peter Gilbert needlessly conceded a free-kick.
However, Wednesday claimed the three points five minutes from the end with a bizarre goal.
Burton found space down the right and Kiraly was well placed to gather the cross, but Leon Cort panicked and stuck out a foot as the ball looped up into the air and landed on the crossbar before dropping on the line for Tudgay to finish with the simplest of goals.