Clinton Morrison fired the Eagles in front on 30 minutes and defender Darren Ward added a second 11 minutes later to lift an otherwise disappointing match.
A scrappy first half saw Palace score twice to bring some cheer to the home fans.
The bitterly cold conditions didn't help as the players had difficulty keeping their balance and no doubt this affected Derby skipper Michael Johnson as he gifted Palace their first goal.
His back pass didn't quite reach keeper Lee Camp who had to leave his area to block Andy Johnson's run but the ball deflected nicely to Morrison who was able to comfortably steer into the empty net from 20 yards out.
After that Palace were struggling and their fans were getting somewhat impatient as passes continuously went astray.
Derby's best chance fell to Danny Graham who raced past Australian defender Tony Popovic to give himself a one-on-one chance with Palace keeper Gabor Kiraly but the Hungarian did extremely well to block his shot.
Dougie Freedman volleyed against the top of the crossbar before Ward added a second for the Eagles.
Jobi McAnuff's corner was allowed to carry to the far side and Ward struck a rising shot for his third of the season.
The second half began as awfully as the first, although Tom Soares should have netted a third when he fired wide after Fitz Hall's low cross fell into his path.
Johnson then made a brilliant run down the right before crossing to Mikele Leigertwood who proceeded to lift his shot over the top.
At the other end Kiraly had to make a flying stop to deny Paul Peschisolido pulling one back.
This inspired the Rams to keep plugging away and useful chances fell to Tommy Smith as well as substitute Adam Bolder, while at the other end Johnson missed a great chance from 10 yards out by firing his shot wide of the target.
It wasn't classic stuff from either side but nonetheless three very useful points for Iain Dowie's outfit.