The Swans made it three games unbeaten under caretaker-manager Alan Curtis following a hard-fought draw against Crystal Palace at Selhurst Park.
Palace - on their best run of form since returning to the Premier League - had the better of the first half without troubling Lukasz Fabianski.
But the Swans goalkeeper was called into action twice in the second period as he kept out efforts from Brede Hangeland and substitute Patrick Bamford.
As the game entered the closing stages, Swansea searched for a winner and they came close as Gylfi Sigurdsson's curling free-kick was well saved by Wayne Hennessey.
The result sees the Swans drop to 17th in the Premier League table with 19 points from 19 matches played.
The Swans made eight changes from the win over West Brom, with caretaker-manager Alan Curtis handing Jordi Amat a first league appearance of the campaign while Marvin Emnes also made his first league start since May.
Midfielder Matt Grimes made his first Premier League start since joining the Swans last January, while Kyle Naughton, Jack Cork, Jonjo Shelvey, Modou Barrow and Bafe Gomis completed the changes.
Crystal Palace were looking to continue what had been a remarkable calendar year in 2015, with Alan Pardew’s side impressing this season in a run which took them up to fifth place in the Premier League prior to this fixture.
Palace also knew a victory could take them into the top four and they made all the early running at Selhurst Park, with Wilfried Zaha causing problems on the flanks and Yohan Cabaye pulling the strings in the centre of midfield.
The visitors - looking to build on the win over West Brom on Boxing Day - had to deal with plenty of early deliveries into the box, with the back four and goalkeeper Lukasz Fabianski coping well with an aerial bombardment.
Swansea reverted to a diamond formation to try and combat the pace of Palace and they looked threatening on occasions as a fine Shelvey through ball just evaded the onrushing Emnes in the Palace box.
The home side made their first substitution at the break as Marouane Chamakh was replaced by Bamford - and it was Palace who came close to taking the lead just three minutes after the restart.
A lovely inswinging free-kick from Cabaye was met by Hangeland but his powerful header was palmed away by Fabianski down to his left.
It wasn't long before Swansea made a double change as Shelvey and Marvin Emnes made way for Ki Sung-Yueng and Sigurdsson as the visitors looked to inject some pace into their attacks.
And it was the visitors who were next to come close on 62 minutes as Barrow cut in from the left before seeing a left-foot strike tipped over by Wayne Hennessey in the Palace goal.
At the other end, opposite number Fabianski had to be alert with 16 minutes remaining as a powerful drive from Bamford was beaten away by the Poland stopper.
The Swans made their third and final change on 77 minutes as Amat was replaced by Kyle Bartley.
As the game entered the final ten minutes, Palace sensed a winner and upped the tempo as Jordon Mutch drove forward before shooting wide of the left-hand post, while Zaha tricked his way past Kyle Naughton before curling his effort a yard wide of the upright.
But it was Swansea who came the closest to winning it in added time as Sigurdsson's 25-yard free-kick looked to be heading for the bottom corner but Hennessey flung himself to his left to palm it away.
CRYSTAL PALACE: Wayne Hennessey, Joel Ward, Brede Hangelund, Scott Dann, Yohan Cabaye, Wilfried Zaha, Mile Jedinak (capt), James McArthur (Jordon Mutch, 75), Pape Souare, Marouane Chamakh (Patrick Bamford, ht), Jason Puncheon (Lee Chung-Yong, 70).
SUBS: Julian Speroni, Fraizer Campbell, Joe Ledley, Martin Kelly.
SWANS: Lukasz Fabianski, Kyle Naughton, Jordi Amat (Kyle Bartley, 77), Ashley Williams (capt), Neil Taylor, Jack Cork, Jonjo Shelvey (Ki Sung-Yueng, 56), Matt Grimes, Modou Barrow, Marvin Emnes (Gylfi Sigurdsson, 56), Bafe Gomis.
SUBS: Kristoffer Nordfeldt, Stephen Kingsley, Jefferson Montero, Andre Ayew.