Saturday's triumph moved the Rams to within five points of the top six.
Palace are also one of a cluster of clubs looking for a late surge to put them into the promotion mix but their 10-game unbeaten league run was ended at Pride Park.
Steven Davies struck early on and Jeff Hendrick scored just before the half-hour mark to give Derby a two-goal lead at half-time.
Theo Robinson's penalty at the start of the second half ensured all three points for Nigel Clough's side despite Chris Martin and Darren Ambrose replying late on for Palace.
Craig Bryson was restored to the Derby starting line up on his return from injury in one of two changes made by Clough.
Bryson missed the defeat at Brighton on Tuesday night with a tight hamstring but returned to replace James Bailey. Ben Davies also came into the Rams' midfield as Nathan Tyson joined Bailey on the bench.
Palace were unchanged from their home victory over Barnsley in midweek.
Davies put Derby in front after six minutes, beating Julian Speroni with a rising shot from close range after linking up with Robinson.
Palace might have responded almost immediately but Glenn Murray put his far-post header straight at Rams goalkeeper Frank Fielding.
Robinson rattled the crossbar with a 20-yarder midway through the first half but Hendrick soon made it 2-0 with a low shot into the bottom right-hand corner from the edge of the box.
Steven Davies was forced off injured shortly afterwards and replace by teenager Callum Ball.
Palace threatened with another header but this time Sean Scannell missed the target to let Derby off the hook.
Fielding made a parrying save to deny Murray after 37 minutes as Palace applied some late first-half pressure.
However, it was the Rams who had the last chance of the half and perhaps Ball should have put the game beyond doubt instead of heading over from six yards out.
The substitute's miss paled into insignificance four minutes after the restart when Anthony Gardner handled Gareth Roberts' cross.
Robinson made no mistake with the spot-kick, firing the ball high into the right-hand side of the net.
Palace boss Dougie Freedman had brought on Jonathan Williams and Dean Moxey at half-time, with Scannell rand Mile Jedinak the players making way, but his plans for getting back into the game were now in tatters.
Bryson fired wide from long range just before the hour as Derby seemingly took their foot off the gas.
However, Martin's goal in the 79th minute soon saw them rediscover their urgency.
Martin beat Fielding with a low, right-foot shot from 12 yards out.
Ball then worked Speroni and Hendrick sent a shot narrowly wide.
Gardner headed over from a Ambrose corner when Palace came forward again.
Ambrose then set up a tense finale when his 18-yard effort made it 3-2 with a minute remaining but Derby held on.