Clinton Morrison put Palace in front on 17 minutes and after Wednesday missed the target on several occasions to get back into it, Glenn Whelan's own goal sealed the points for Iain Dowie's side 12 minutes after the break.
Paul Sturrock's outfit were woeful in front of goal and underlined why they have just notched six goals this season.
Palace edged both halves although on ten minutes Chris Brunt rifled a ferocious free-kick which Gabor Kiraly had to save at the second attempt.
Ben Watson went close for the home side before Clinton Morrison headed them in front. Marco Reich, on a three-month contract, floated over a perfect cross to beat Dougie Freedman who in turn cleverly headed across goal for Morrison to bag his fourth goal in five.
Chances were on offer at both ends with David Graham firing over the crossbar from not too far away and at the other end Tom Soares went wide and a few minutes later fetched another effort over the bar.
Then Burton O'Brien wasted another chance as he forced Kiraly into making a desperate save on the stroke of half-time.
Straight from the re-start Chris Eagles let fly a tremendous free-kick 25 yards out which Kiraly miraculously turned over the bar but Palace did not have to wait long to finally kill off the Yorkshire side.
Reich played in Jobi McAnuff who travelled along the byline before setting up Emmerson Boyce. The Palace defender's header was not particularly powerful but it was enough to get a deflection off Wednesday skipper Whelan before dropping tamely into the corner of the net.
After that Lee Peacock had a couple of chances, while Watson and Freedman likewise for Palace, but in the end Palace deserved the points to get their first win in four matches and climb a few places up the table.