A 61st minute goal by Tommy Black was enough to give Palace their first league win of the year and Derby could not manage a shot on target in reply.
The home fans chanted "what a load of rubbish" long before the end and are clearly running out of patience with manager John Gregory.
Derby must have sensed it was going to be one of those nights when Lee Morris pulled up with a hamstring injury in the pre-match warm-up and they could have been down to ten men after just six minutes.
Goalkeeper Lee Grant was very lucky not to be sent off when he fouled Black outside the area but referee Tony Leake let him off with a yellow card.
Palace exploited a nervy opening by Derby and almost took the lead when Shaun Derry struck the bar with a 25-yard free kick in the 17th minute.
But Derby recovered and Everton's on-loan striker Lee Chadwick shot into the side netting before Cedric Berthelin denied him in the 34th minute.
The Palace keeper was forced to dive to his left to beat out a Craig Burley volley in the 44th minute but he was rarely threatened after the break.
Black got the decisive goal when he got in between two defenders to head in Julian Gray's cross from eight yards and Palace could have had more goals after the break.
Black also shaved a post with a swerving free kick but Derby managed little in reply and the final whistle could not come soon enough for their frustrated fans.