The Georgian international pounced eight minutes from time to sink Trevor Francis' Eagles just when the Palace boss thought his side had turned the corner.
Palace edged a very ordinary first half with Dougie Freedman and Andy Johnson going close to give the home side an early lead.
The Rams remained on the back foot and indeed took 44 minutes before Adam Bolder became the first player to test the clean gloves of Aleks Kolinko.
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If it was at all possible, the second half got worse. Palace's star youngster Wayne Routledge was well watched and it was the visitors that looked more likely to score.
After 70 minutes Kolinko spilled Adam Murray's free-kick and was grateful to see the ball bobble wide of the post while Kinkladze missed an absolute sitter on 75 minutes.
But the clever Derby midfielder made no mistake seven minutes later. Lee Morris accelerated down the left and crossed into the goalmouth for Kinkladze to pounce with a low left-foot shot from eight yards out