Despite less than 72 hours earlier demolishing Valencia at the Mestalla, the Welsh side showed no sign of a Europa League hangover as they eased to a 2-0 win at Selhurst Park.
Palace were left chasing shadows from the outset, with Michu's strike after 80 seconds followed by a Nathan Dyer effort moments into the second half.
It could - and should - have been a much larger margin of victory for Swansea, with that the only frustration for manager Laudrup after the match.
However, following Monday's hard-fought draw with Liverpool and the win in Spain, the Dane's overriding emotion was pride after winning at Selhurst Park.
"It has been a fantastic week," Laudrup said. "Before the start, I thought this particularly would be the most difficult game because it was on the back of Liverpool and Valencia.
"This was the third game in only six days, with the travelling and all that. You have to play an away game here against a different type of football, more direct.
"I thought this was going to be the most difficult game, so I am really pleased with what the players did today.
"It always helps when you score in the first minute, but even so you have to play over 90 minutes.
"I thought we really dominated the game from the first to the last second.
"The only thing is, we should have scored more goals because we had the chances to score five or six like we had on Thursday, but it is of course difficult not to be pleased when you win 3-0 and 2-0 in just three days."
One of the best performers in that six-day period has been Michu.
After starring for Swansea last season, the 27-year-old began this season comparatively slowly - until this week, that is.
Michu netted against Liverpool and Valencia, before producing a man-of-the-match display in south London.
"I don't know if he is back to his best, because what is his best?" Laudrup asked.
"I don't look at him as just a goalscorer because for me he is not even a centre-forward. He has always been an offensive midfielder than can score goals, but can also play as a centre-forward.
"I don't look at Michu just as a goalscorer so I don't see it as a problem when he does not score for three games."
Michu's form last season saw him rewarded with a new and improved four-year deal in January, just six months after moving to the Liberty Stadium.
Despite that, speculation was rife over the summer that a bigger club could swoop for the Spaniard - not that Laudrup was ever worried.
"What is so important when you talk about interest from other clubs, the most important thing is what the player wants," he said.
"I know you have a contract and all that, but it is important what the player wants and then secondly what the club says.
"There have been some cases during the summer at other clubs, but Michu wants to stay.
"He wants to stay after his first season because he wanted to participate in the second year, with Europe and with everything.
"What happens in the future, next year? I don't know. But I think it is so important what the player wants and I don't think Michu had any doubts that he wanted to stay here this season."
Michu was one of a number of impressive players for Swansea, who Ian Holloway described as "embarrassingly good".
The Palace manager kept his players in the changing room after the match for a dressing down, although he shoulders the lion's share of the blame after being forced to watch from the stands due to a touchline ban.
"I am absolutely gutted," he said. "If you had seen the work we did, what we talked about and how sharp we were, I was excited then it all faded away in about one minute 30 seconds, didn't it?
"The changes I chose or had to make with the new lads coming in and it looked like they were strangers.
"With the greatest respect, that is as bad I ever want to feel sat here. I didn't enjoy any minute.
"It was my fault not being on the line with them, for losing my temper against Tottenham. I felt estranged and out of it and they have to feel the manager is with them, so please blame me.
"I needed to be there today and they'd have felt a little bit more confident, we would have got a little tighter to things.
"When the manager is there it is a little bit different so I would rather blame myself."