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The loss leaves the Rams in the play-offs, and on the form they showed at Selhurst Park, they are unlikely to be joining English football's elite next term.
Only a victory at the mid-table Eagles would have kept Derby's top-two hopes alive, but they produced one of their most insipid performances of the campaign as Peter Taylor's side cruised to an unexpectedly easy victory.
After a scrappy opening to the game, Palace took a 29th-minute lead with their first worthwhile attack of the encounter.
Former Birmingham striker Clinton Morrison scored the opener when he latched on to Carl Fletcher's poor long-range shot. His misplaced effort was picked up by the unmarked forward just inside the penalty area and he stroked his shot past Lee Camp in the Rams goal.
Morrison flashed another shot wide just two minutes later as the Eagles started to get on top.
When the visitors tried to respond, Steve Howard headed Darren Currie's left-wing corner just over the crossbar before captain Matt Oakley shot straight at Julian Speroni.
Derby were poor in the opening 45 minutes but if anything they were even worse after the break.
Their cause was not helped when Giles Barnes limped out of the action early in the second period after appearing to suffer a knee injury and had to be replaced by Arturo Lupoli.
But defensively they were ragged and Camp was forced to make a diving stop to keep out Ben Watson's shot before Jobi McAnuff burst clear only to drag his effort wide.
Palace deservedly doubled their lead in the 67th minute when a completely unmarked Mark Kennedy was allowed to run forward before lashing a left-foot shot past Camp.
Speroni made a good scrambling save to keep Lupoli's late effort out in a rare Derby foray upfield, but the visitors ended the game a demoralised and well-beaten side.