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The Eagles' leading scorer grabbed a 55th-minute winner for Neil Warnock's side as they bounced back from last weekend's humiliating 4-0 home reverse to Scunthorpe.
But the south London side were indebted to keeper Julian Speroni, who made two superb saves in the second half to ensure Derby slumped to a fourth successive defeat.
Speroni was lucky to escape a red card after 19 minutes when he picked the ball up outside his penalty area, only to escape with a booking from referee Michael Oliver.
And the Eagles number one immediately made a save as he tipped over the resultant free-kick fired goalwards by Gary Teale before also denying Jake Livermore after he was played through by on-loan Everton striker James Vaughan.
Palace posed more of an attacking threat as the first half wore on and Ambrose's corner was prodded wide of the post by Paddy McCarthy.
Ambrose missed a great chance to put the home side in front before the break, firing wildly over the bar from five yards out after Alan Lee had headed Danny Butterfield's deep cross back across the face of goal.
Just 60 seconds later Butterfield produced another inviting cross and Alan Lee's header forced Derby keeper Stephen Bywater to make a scrambled save at his near post.
Palace went in front on 55 minutes. Shaun Derry won a header on the edge of the box and Ambrose produced a neat finish, clipping it with his right foot past the advancing Bywater.
The goal settled the Eagles and they looked the most likely to add a second - and almost did when Johannes Ertl's thundering header from Ambrose's free-kick crashed off the bar.
But Derby did pile on the pressure in the closing stages - only to find Speroni in inspired form. He produced an instinctive stop when he parried away Rob Hulse's header from Lee Croft's header with six minutes left.
But Speroni's best save was kept until the end of the match when he dived full length to his left to turn Kris Common's low strike around his right post.