But a second league win of the campaign, achieved with a controlled display, betrayed no signs of complacency, Laudrup's side going ahead as early as the second minute with a crisp passing move.
Ex-Palace winger Wayne Routledge received the ball from Michu, who had dropped deep into a pocket of space in midfield, and threaded a neat pass to midfielder Shelvey.
Michu peeled round the back of the Palace defence and was found by Shelvey - via a deflection off Routledge - and the Spaniard poked his shot through the legs of goalkeeper Julian Speroni and into the net.
Swansea were almost two up moments later when Shelvey's corner picked out defender Chico Flores at the back post, but his side-footed volley came back off the post.
Crystal Palace boss Ian Holloway, confined to the stands
because of a touchline ban,
looked on as his side failed to find a way through a congested midfield as Swansea packed men behind the ball.
Swans at the double
Swansea have scored two or more goals in three successive Premier League games for the first time since December 2012.
Michu continued to pose a threat to the Palace defence with his movement, and was unlucky with a deflected shot from the edge of the penalty area that whistled inches over the crossbar.
Palace's best hope of a goal in the first half seemed to be from set-pieces, and a rehearsed free-kick routine saw Adlene Guedioura strike a shot from distance that Swansea goalkeeper Michel Vorm had to save.
Swansea, who only won one game against the promoted clubs last season, kept Speroni busy in the remainder of the half and Angel Rangel's sweetly struck volley forced the Palace keeper into a spectacular diving save.
The visitors' dominance continued after the break with Michu at the heart of it as they controlled possession and opened up Palace time and again.
Inevitably Michu had a hand in the second goal three minutes after half-time when he brilliantly spun the Palace defence to release Alvaro Vazquez.
Ian Holloway 'upset' by poor Palace
Vazquez, making his debut following a
season-long loan move from Spanish side Getafe,
saw his shot from a tight angle saved by Speroni, but the Spaniard seized on the rebound and pulled the ball back for Dyer, who finished emphatically from close range.
Michu had the ball in the net again before the final whistle, after latching on to a through-ball from substitute Jonathan de Guzman, only to be flagged offside.
Crystal Palace boss Ian Holloway:
"I can't see a positive thing. We were awful, so I am very disappointed.
"I think we were completely outplayed by a better team and there is a lot of work for us to do.
"I had a little go at the players because they need to show that fight and desire. We maybe showed Swansea too much respect."
Swansea boss Michael Laudrup:
"It's been a great week. It's our third game in just six days and an important win for us.
"Overall I have to very pleased with a game I felt we dominated from start to finish.
"What we are trying to do is use the squad and I made four or five changes because I need everyone to contribute."
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