The Welsh side dominated proceedings in west London as they began life without Brendan Rodgers in some style.
Only eight minutes were on the clock when Michu struck the first goal of the Premier League season.
The Spaniard collected a loose ball on the edge of the box and unleashed a low shot that, while well struck, should have been dealt with by Rob Green.
Michu then hit the crossbar as half-time approached after fellow summer signing Chico had done the same, before Laudrup's side ran away with proceedings in the second half.
First Michu exquisitely curled home a left-footed strike, before Nathan Dyer netted twice and Scott Sinclair came off the bench to lash home a fifth.
So much had been expected from QPR fans coming into the game after the club brought in eight new faces in a bid to avoid the struggles of last season.
Green, Fabio and Junior Hoilett were among those to move to W12 and were all handed their debuts on Saturday afternoon.
The biggest arrival of the summer was undoubtedly that of Manchester United's Park Ji-sung, who was handed the captain's armband on his first QPR appearance.
Swansea themselves included three debutants in their starting line-up and it took just eight minutes for one of those to make an indelible mark.
The Swans broke forward after an end-to-end start and Michu collected a loose ball to hit home a low shot from 22 yards.
However, as well as Michu struck the ball, much of the blame falls on Green as he let the long-range strike squeeze into the corner when it looked easier to save.
Another Swansea debutant to make an important early impact was defender Chico, who cleared off the line after Michel Vorm fumbled a close-range Jamie Mackie shot.
It was the first of a flurry of QPR chances as Hoilett then wriggled down the left, cut inside and unleashed a right-foot strike that went just wide of the far post.
Mark Hughes' side continued to press with Adel Taarabt and Fabio next to get shots away, before Hoilett rose highest to meet a cross from the latter.
The former Blackburn man's header went just wide and Taarabt followed it up moments later with a fierce drive that was easily dealt with by Vorm.
However, the Swansea goalkeeper had to do much better to thwart the Morocco international's next attempt, which had looked set for the bottom right-hand corner.
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For all of QPR's attacking endeavour, though, they looked shaky at the back as the first half came to a close.
First Jonathan de Guzman, another of Swansea's summer signings, fired an ambitious 35-yard free-kick that forced Green to scurry across his goal and palm wide.
Chico rattled the crossbar with a header from the resulting corner, before Michu hit the goal frame in a penalty-box melee at another corner.
Half-time allowed Hughes to give his side a pep talk but it did not work as Swansea went on to run riot.
After Hoilett saw a penalty appeal waved away during a bright QPR start, Michu doubled Swansea's advantage eight minutes into second period.
Former QPR winger Wayne Routledge ran at the home defence and passed to the former Rayo Vallecano man, who - despite being unbalanced - curled a superb left-footed strike into the top corner.
That was just the start of it for the Rs as they fell further behind 10 minutes later, with Dyer collecting the ball in space and slotting home past Green.
And in the 71st minute the visitors boasted a four-goal cushion as substitute Kemy Agustien fired a great ball over to Dyer, who showed good control and then slotted home from close range.
The home fans were stunned into silence and things got worse as the visitors made it 5-0 in the 81st minute.
The QPR defence were all over the place and substitute Sinclair found space to fire home in front of the Loft End.
"Boring, boring Swansea" rang around Loftus Road from the away end and Danny Graham came close to making it six with a shot that just went across the face of the goalmouth - sparing QPR supporters anymore pain.