Wednesday came out the blocks faster and David Prutton was unlucky to see his volley from Danny Pugh's cross go just over the bar.
The Owls kept up the pressure and Kieran Lee was unlucky to see his effort cleared off the line by Damien Delaney, who made a last-ditch block.
Palace had a great chance to take the lead just before the break as Stephen Dobbie found space on the edge of the area but his goalbound shots were blocked by the Owls defence.
Dobbie was in the action again shortly after the restart, as he was denied in front of goal this time by a good save from Chris Kirkland who parried the ball behind for a corner.
The visitors were beginning to exert some serious pressure on the Owls' goal and Kirkland had to be at his best again to save from Yannick Bolasie and gather the rebound.
These missed chances were to cost Palace as Wednesday took the lead through Lita who headed home Lewis Buxton's cross from close range to seal the points for his side.