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The reward for winning at Stoke City in midweek was a two-leg semi-final against Manchester United, but Derby will not trouble the Premier League giants on the evidence of this feeble display.
Manager Paul Jewell conceded that his side was second best in every way, even though Palace's second-half winner looked offside.
Derby simply did not have enough drive and invention to threaten a well-organised and committed Palace team that is starting to find the momentum that took the club to the play-offs last season.
The impressive Ben Watson dominated midfield and centre-half Paddy McCarthy played on with a broken nose after his stunning early strike set the London club on their way.
McCarthy found himself with the space to line up a shot in the third minute and his right-foot drive sailed over Roy Carroll and into the top corner.
The only threat to Palace's dominance was goalkeeper Julian Speroni, who had already escaped when he fumbled a corner.
But a minute later a free-kick was headed-on by James Tomkins and Luke Varney beat Speroni to the ball to head in.
Palace regrouped and regained the lead in the 61st minute when Clint Hill released Craig Beattie on the left and his low cross was slid in by Shefki Kuqi.
Palace wasted two or three good openings to wrap up victory, but Derby had little to offer and never threatened to draw level for a second time.