The Owls dominated the first half but failed to make their domination count and it looked like they may have missed their chance as Palace bossed the second period.
But Leroy Lita popped up inside the final 10 minutes to head home Michail Antonio's cross for his third Wednesday goal following his loan move from Swansea last month.
That was enough to extend their unbeaten run to seven Championship games and after spending much of the first half of the campaign in the bottom three, Owls boss Dave Jones may now be able to look up the table.
For Palace, their away-day blues show no sign of abating as they are now without a win in 10 matches on the road and missed the opportunity to close in on the automatic promotion places.
Wednesday created little in Tuesday's stalemate at Birmingham, but they were quick on to the attack this afternoon with David Prutton almost putting them into an early lead.
Danny Pugh made headway down the left and after his cross was cleared to Prutton, the midfielder lashed a half-volley from 25 yards, which flew just over the bar.
The Owls continued to press as Lita headed straight at Julian Speroni following good work from Kieran Lee, who then went even closer as his volley was blocked on the line.
Antonio was back to his best for the Owls after a period of poor form and he terrorised the Palace defence, though Wednesday were just unable to get make the breakthrough.
Owls goalkeeper Chris Kirkland was called into his first meaningful action of the afternoon to keep out Stephen Dobbie's half-volley following good work from Jonathan Smith's direct run.
Palace continued to be the better side, but they were hit by a sucker-punch in the 81st minute when Lita rose highest to head home the impressive Antonio's cross which went in off the underside of the bar.
Ian Holloway's men had little by way of a response as Wednesday held on with ease.