The Eagles were hit with a 10-point penalty by the Football League for going into administration earlier this week - the deduction meaning they are now involved in a desperate battle against the drop.
But a fired-up Palace were too much for basement club Peterborough - who are yet to win away this season - as they roared to a comfortable victory.
Posh had the first chance of the afternoon when Chris Whelpdale's header from a George Boyd corner was headed off his own line by Nathaniel Clyne.
But the visitors did not look totally comfortable at the back and Danny Butterfield smashed a shot just past the post after dispossessing Tom Williams and then his cutback was mis-kicked by the normally reliable Darren Ambrose.
But Palace did take the lead in the 28th minute as Danns hooked in from 10 yards out after Clint Hill's driven ball to the right of the box was nodded on by Alan Lee and Butterfield.
The Eagles saw a strong penalty appeal waved away in the 36th minute when Lee appeared to be pushed by Jake Livermore.
Palace spurned an early chance to move further ahead in the opening minutes of the second half when Butterfield lashed the ball over from close range after a Lee Hills long throw dropped at his feet.
But Danns got his second of the afternoon shortly afterwards. It started with Hills breaking forward down the left before squaring to Ambrose.
He produced a lovely chip over the Posh defence and Danns calmly rolled the ball past Joe Lewis for his sixth of the season.
Butterfield was unlucky not to cap a fine display with a goal and went round Lewis after Ambrose threaded a ball into his path, but from a tight angle he could only shoot into the side-netting.
Peterborough's only response in the closing stages was George Boyd's low strike which Julian Speroni had to go full-stretch to get a hand to.