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Shefki Kuqi's cool finish handed Neil Warnock's men the lead after teenager Victor Moses was given his marching orders for a second yellow card.
The result leaves Derby nervously looking over their shoulder at the relegation zone with three games left to play.
Rams skipper Paul Connolly cleared from under his own bar from Anthony Stokes' cross in the 16th minute before Gary Teale flashed a header across the face of his own goal from the resulting corner.
Johannes Ertl then mis-timed his strike from the edge of the box before Paddy McCarthy fired a snap-shot wide.
Kris Commons missed Derby 's best chance of the half in the 38th minute, firing straight at Julian Speroni with a clear sight of goal.
If the opening period was a dour affair, then the second was anything but.
Speroni was forced into two superb stops from goalbound Commons strikes as the Rams' prize asset began to show why he is being tipped for a top-flight move.
Rob Hulse then hit the crossbar with a towering header in the 56th minute as Derby gained the upper hand.
And in the 60th minute, Nigel Clough's men were handed another boost when Moses, who had previously been booked for diving, was controversially sent off for a second bookable offence when referee Mr Woolmer adjudged that the forward had fouled Miles Sterjovski despite clearly taking the ball.
But the injustice seemed to stir the home side into action and Kuqi capitalised on some poor defending in the 63rd minute to lift his effort over the stranded Stephen Bywater to give Palace a lead.
And a resilient Palace held on for all three points but had to withstand a few nervy moments - none more so than when Emanuel Villa saw his late header ruled out for offside.