In a frenetic opening, Jason Scotland had a good effort saved by Julian Speroni inside three minutes, before transfer-listed Paul Ifill forced Swans keeper Dorus de Vries into tipping his rasping 16-yard effort over the bar on five minutes.
Swansea saw plenty of the ball but failed to get in behind the well-drilled Eagles back four and it was Ifill again who nearly hit City with the classic sucker punch on 24 minutes when he latched onto Jose Fonte's flick, but could only shoot straight at de Vries from 10 yards with a clear sight of goal.
Eagles boss Neil Warnock was forced into two early changes with the injured John Oster and James Scowcroft being replaced by Kieran Djilali and Calvin Andrew respectively in the first half.
And it was the incident involving Scowcroft that led to Palace taking the lead.
After Leon Britton smashed into the Eagles striker on the left hand touchline forcing Scowcroft off, Watson's in-swinging cross from the resulting free-kick flew past de Vries and into the far right-hand corner to hand Palace the advantage.
Ifill again went close two minutes before the break but his right-footed strike from Djilali's deep cross flew wide, before Scotland stung the hands of Speroni from the edge of the box on the stroke of half-time.
Roberto Martinez's side came close to equalising eight minutes into the second half, but Mark Gower's firm shot from just inside the box was well turned round the post by Speroni.
Palace should have doubled their lead just a minute later after Ashley Williams made a hash of Ifill's hopeful long ball leaving Andrew to bear down on goal, but the Eagles striker could only shoot wide.
And Darren Pratley should have made Palace pay for that missed chance after Scotland found the midfielder with space in the six-yard box to pick his spot only for Speroni to somehow get a hand to the ex-Fulham man's strike to keep the home side's lead intact.
The Argentine's heroics were underlined 11 minutes later when Palace doubled their lead after Carle smashed a low 20-yard drive past de Vries for his third of the season to end any hopes the Welsh side had of taking something from Selhurst Park.