The Swans showed no sign of a Europa League hangover in the capital as they outplayed a poor Palace side.
Fresh from demolishing Valencia at the Mestalla, Michael Laudrup urged his players to re-focus on their return to domestic action at Selhurst Park.
They did just that, and in some style, outclassing the Eagles from the outset in a 2-0 win that in no way reflected their dominance.
It took just 80 seconds for Michu to set Swansea on course for a fourth consecutive win against Palace, rifling home.
Palace boss Ian Holloway would have been forgiven for watching the first half through his fingers, with Chico Flores rattling the post moments later, before Michu and Angel Rangel came close to netting.
The Welsh outfit would not be denied for long, though. With no defenders on the Palace bench and Damien Delaney forced off injured, it was all too simple for Nathan Dyer to fire home after debutant Alvaro Vazquez's shot was saved.
Vazquez wasted a chance to extend their lead further as the game petered out, with Swansea securing a win with worrying ease for the south Londoners.
The visitors made five alterations following their trip to Spain, with Wayne Routledge coming in against the club with whom he started his career.
Routledge was reminded of that decision from the outset by the home support, who were cursing poor defending after just 80 seconds.
Ending a move he started, Michu collected a pass from Jonjo Shelvey, via a slight deflection off Routledge, and lashed home through Julian Speroni's legs.
Swansea should have had a second inside four minutes after Chico capitalised on more sloppiness at the back, only to see an effort come back off the post.
As well as struggling to cope with Swansea's attacking threat, the Eagles were failing to produce any chances of their own.
Jason Puncheon saw a potentially-threatening free-kick blocked, while the Swansea defence cleared after Michel Vorm flapped at a Barry Bannan free-kick.
The hosts were soon on the back foot again as Routledge pulled the ball back for Michu, whose thunderous strike flew just over thanks to a slight deflection off Danny Gabbidon.
The Spaniard nodded over from the resulting corner, while there looked to be a decent penalty appeal against Moxey after the recently-booked full-back handled a Shelvey cross.
Speroni then palmed away a superb Rangel volley from the resulting corner as Swansea continued to look a class above.
It was not until the 37th minute that Palace managed to test Vorm for the first time, although Adlene Guedioura's long-range strike was easily dealt with.
Their best chance of the half came towards the end, with a fine Adrian Mariappa cross set to find Cameron Jerome at the back post until Rangel's late interception.
It was a miserable opening 45 minutes for the hosts, which got even worse when Delaney went down injured.
The Irish centre-back was unable to return for the second half and had to be replaced by midfielder Jose Campana as Palace had no defenders on the bench.
It meant captain Mile Jedinak was forced to play as makeshift centre-back and that alteration reaped immediate rewards for Swansea.
After Speroni saved Vazquez's initial effort, the debutant pulled back for Dyer and the diminutive winger rifled home three minutes after the restart.
When attentions returned to the football, Vazquez wasted a glorious chance to put Swansea ahead, scooping over after from neat team interplay.
Puncheon twice failed with hopeful efforts as Palace attempted to claw one back, but it wasn't to be and the game petered out.