There were some initial positive signs for the visitors. Emmanuel Adebayor linked well with Wilfried Zaha during the early stages of his first start for his new club.
However, the Togo international played a key part at the wrong end as his foul allowed Sigurdsson to give Swansea the lead.
The Iceland international made full use of the opportunity to score his fifth goal in six games.
Swansea should have doubled their lead less than two minutes later. Alberto Paloschi, making his first start for the Welsh club since his £8million arrival from Chievo, narrowly failed to connect with Routledge’s cross and Damien Delaney needed to be alert to block Ayew’s follow up effort.
Adebayor headed a Yohan Cabaye free-kick wide at the opposite end, but it was rare relief for Palace, who were struggling to contain Swansea in the wide channels, with Pape Souare particularly adrift.
Ayew spurned a further chance to extend the Swansea advantage by turning a Sigurdsson corner narrowly wide at the far post, with Routledge executing a poor miss of his own by dragging Jack Cork’s astute pull-back across the face of goal.
Such profligacy nearly proved costly as Adebayor poked Zaha’s pass over, and Dann flashed a header wide from Joel Ward’s free-kick.
There was no such let-off for Swansea two minutes into the second half. Cabaye’s corner was flicked on by Delaney and Dann slid home from close range for just Palace’s second Premier League goal since December 19.
It sparked a bright Palace spell, with substitute Marouane Chamakh failing to turn in a Jordon Mutch lay-off as Swansea were set on the back foot.
More chances came during a chaotic finale, with Ashley Williams having a header blocked on the line and Modou Barrow firing narrowly over.
- Telegraph