Illness affected both teams prior to the Boxing Day clash at Selhurst Park but Palace came out on top. A brace from Jose Fonte in the first half was added to by Danny Butterfield late on. Gary Doherty scored Norwich's goal in the first half to cancel out Fonte's opener.
Palace boss Neil Warnock said: "I don't usually get wins over Norwich at Christmas; I usually get draws or defeats but I am delighted with the win.
"They are not a bad side and that makes it even sweeter, really.
"The lads really 'gritted' in and, like me, some of them were under the weather with the flu lurking round, but all credit to them and it was great to see the third goal go in."
Defender Paddy McCarthy was substituted early in the second half and his troublesome shoulder injury may need to be operated on.
That could force Warnock to enter the transfer market next month.
He added: "I am going to have to speak the chairman about the situation, as he (McCarthy) is likely to need an operation some time in January, which will leave us short at the back.
"We may give him one more go but we will have to see."
The result left Norwich without a win in 20 successive trips to the capital.
The Carrow Road club have not won at a London ground since a 2-0 victory at Millwall in March 2003.
Boss Glenn Roeder told the club's official website, www.canaries.co.uk: "It's hugely frustrating.
"Yet again, we have more than matched our opponents away from home and, yet again, we feel we have done enough to come away with something from the match.
"But the manner in which the first two goals was conceded simply isn't good enough. We gave them far too much space from the first free-kick and we were sloppy on the second.
"I call it professionalism - you need to have the professional's ability to read a situation like a possible quick free-kick and we didn't.
"Now we have to pick ourselves up and get ready for Forest on Sunday."
Roeder said midfielder Lee Croft was absent due to illness, adding: "Lee has been feeling unwell.
"We didn't want to risk him giving something to anyone else as that would be the last thing we need.
"Hopefully he'll be back in the mix for the Forest game and everyone else came through okay."