Michu put the visitors ahead after just eight minutes in a first half mostly controlled by QPR, but the midway lead could have been greater after the woodwork was rattled twice shortly before the break.
There was no such home team control in the second 45, however, as Laudrup's men ran riot.
Michu's second, also eight minutes into the half, was followed by a clinical double from Nathan Dyer and a fifth in the closing 10 minutes from substitute Scott Sinclair - widely expected to leave the club before August 31 - capped a capital capitulation from the flabbergasted West Londoners.
Both sides, survivors last season following promotion to the top flight in 2011, were hard to recognise amidst a sea of new personnel as they began their bids to consolidate Premier League status.
The two arrivals from Manchester United helped Mark Hughes’ men control large passages but with less than 10 gone it was a Swansea new boy grabbing the spotlight.
After Wayne Routledge’s adventurous foray towards the Rs box was bravely cut out by Anton Ferdinand, Michu pounced on the loose ball to hammer the opener low beyond Rob Green and become the first Spaniard to net the inaugural Premier League goal of any campaign.
A touch of good fortune almost led to an equaliser just two minutes later, but after a desperate clearance from Ashley Williams hit Jamie Mackie and fell at the winger’s feet, he was unable to find a way past Michel Vorm in the impromptu one-on-one.
The home side continued to press their guests in search of a way back into the match, with another debutant, Junior Hoilett, almost lobbing Vorm with a quick-thinking header halfway through the period.
For all of Rangers’ control, however, Swansea were proving more of a threat in smaller doses and hit the crossbar twice in the final five minutes of the half with successive corners via Spaniards Michu and Angel Rangel.
Hoilett dazzled within the first post-intermission minute with a great dribble down the left before a give-and-go with Taarabt set the former Blackburn man up inside the penalty area.
He swiftly went to ground under pressure from Rangel, but referee Lee Probert felt the fall came far too easily and ignored the home stands’ cries for a penalty.
Though the Hoops continued to attack in the early stages of the second, it left them prone to counter-attacks and on 53 minutes this shortcoming doubled their deficit.
Swansea moved swiftly after defending a corner and Routledge weighted his square pass inside from the left perfectly for Michu to latch on and majestically curl in his – and his side’s – second.
It all began to unravel for Hughes’ troops from there. The visitors were high on confidence and after weathering a scrappy period filled with bookings, another lightning breakaway left Dyer clean through to sweep in a third.
After Michu and Danny Graham worked well together to almost conjure a goal for the latter, number four came with 19 minutes left as Kemy Agustien raked a pinpoint ball into the QPR area within seconds of being introduced for Dyer to deftly touch in his second.
The introduction of Sinclair in place of Dyer shortly afterward provoked a mixed reaction from the travelling Jack Army supporters, but the forward – linked with a move to league champions Man City – would add to the feelgood factor nine from time when he casually placed number five beyond the luckless Green.
Chants of “you’re getting sacked in the morning” rang out in the direction of a beleaguered Hughes, while his Danish counterpart couldn’t have felt any more different with a result and performance which will hold up well in the face of predictions of a Swansea survival scrap.
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