Marcus Tudgay's late volley sent Palace crashing to a second successive defeat and finally extinguished any flickering play-off hopes among die-hard fans.
Wednesday striker Tudgay thumped home his 10th goal of the season following Palace defender Leon Cort's mistake to extend the Yorkshire side's unbeaten run to seven matches.
Brian Laws' side have won four and drawn three league matches during that sequence and look a good bet to make the top 10 with a strong finish to the season.
Deon Burton also fired his 10th goal of the campaign to give the Owls an early second-half lead, with Clinton Morrison appearing to have earned a point for Peter Taylor's side with 10 minutes remaining.
Jobi McAnuff (hamstring) and Matt Lawrence returned to Palace's starting line-up with Mark Kennedy and Paul Ifill, also back from injury, named on the bench.
Frank Simek's suspension prompted Wednesday skipper Lee Bullen to switch to right-back and Steve Watson to drop back to central defence, with Kenny Lunt stepping up from the bench to fill the gap in midfield.
McAnuff almost fashioned an early opening for Palace, but his cross was headed wide by James Scowcroft, while Owls midfielder Chris Brunt's shot was comfortably held by Gabor Kiraly.
The Palace goalkeeper then kept out Steve MacLean's shot from inside the area with his feet, but Palace hit back with Morrison twice threatening to open the scoring.
His first goalbound shot was blocked by Watson and his second effort from a similar position forced visiting goalkeeper Turner into a fine save.
Turner then tipped Mark Hudson's 18-yard drive over the crossbar and parried the same player's header from Ben Watson's corner as Palace threatened to make the breakthrough.
Gary Borrowdale fired over the crossbar and another Morrison shot was held by Turner.
Kiraly was well-placed to catch Burton's shot after the break, while Turner held a 30-yard drive from Palace defender Cort.
But Hungarian goalkeeper Kiraly was helpless to keep out Burton's 57th-minute header from Brunt's left-wing cross.
Burton placed his header in the bottom corner from six yards to notch his 10th goal of the season.
Kiraly then denied Tudgay and Burton in quick succession before Shefki Kuqi, an earlier replacemnt for McAnuff, tested Turner from 35 yards.
Kennedy was sent on by Palace manager Peter Taylor for Scowcroft and although the visitors threatened again through Burton, whose 12-yard shot flew wide, the Irish winger was quick to make his mark with his right-wing cross setting up Morrison for the equaliser.
Morrison lashed the ball home right-footed into the roof of the net from close range, but Palace enjoyed parity for only five minutes.
Palace defender Cort sliced an attempted clearance onto his own crossbar and Tudgay slammed home his volley from six yards as Wednesday clinched their eighth away win of the season.
Teams:
Crystal Palace Kiraly, Lawrence, Hudson, Cort, Borrowdale,McAnuff (Kuqi 59), Watson (Ifill 52), Fletcher, Soares,Scowcroft (Kennedy 70), Morrison.
Subs Not Used: Speroni, Butterfield.
Booked: Lawrence.
Goals: Morrison 80.
Sheff Wed Turner, Watson, Bullen, Wood, Gilbert, Tudgay, Lunt,Whelan, Brunt (Spurr 87), MacLean, Burton (Folly 86).
Subs Not Used: Adamson, Hills, Lekaj.
Booked: Brunt.
Goals: Burton 57, Tudgay 85.
Att: 21,523
Ref: A Hall (W Midlands).