Swans keeper Fabianski also came up with a stellar save to keep out Brede Hangeland's glancing header early in the second half while Palace gloveman Wayne Hennessey hardly had anything to do in South London.
The draw saw Alan Pardew's Palace remain fifth on the table as Alan Curtis' Swansea stayed 17th.
- Palace lacking some cutting edge up front. Does Pardew need a new striker in January or do they just have to wait for their current forwards to find form?
- Swansea beginning to show signs of improvement after a poor run. Curtis has made them tough to break down but they may need some help up forward having scored just two goals in their past five outings.
QUOTES: @joelward20 takes the positives from #CPFC's 0-0 draw with @SwansOfficial. Read - https://t.co/b2Yl3xIGp3pic.twitter.com/jBKFX49Nw0
— Crystal Palace FC (@CPFC) December 28, 2015
REACTION: @Matt_Grimes8 delighted to make first @premierleague start for #Swans today - https://t.co/9VA0lnEvFQpic.twitter.com/8qKU3t7qEG
— Swansea City AFC (@SwansOfficial) December 28, 2015
Palace's Pardew on his side's first half of the season:
"We've got 31 points after 18 games: wow. That's fantastic for us.
"Now we've got to hope some of our strikers come back to us.
"You could tell it was our second game in three days. We lacked a bit of imagination and flair."
Swansea caretaker Curtis on his future:
"Nobody's said anything to me, we're just carrying on as normal.
"And now we're just looking towards next weekend.
"The club are in the process of I think interviewing people, or certainly looking at potential candidates."
*Thanks to Opta
8 - Swansea have made eight changes to their starting XI today, the most by a Premier League club this season. Tinker.
— OptaJoe (@OptaJoe) December 28, 2015