QPR remain four points adrift at the foot of the Premier League as their five-match unbeaten run came to an abrupt end at the Liberty Stadium.
They were 2-0 down inside 18 minutes, Michu following up Nathan Dyer's shot and Angel Rangel stroking home after Julio Cesar parried his first effort.
Rangers substitute Bobby Zamora replied from a keeper's fumble after the break.
But Pablo Hernandez weaved through to score from an acute angle and Michu hit Swansea's fourth with a deft finish.
Although they made some expensive additions during the transfer window, with one goal in four league matches Harry Redknapp's team could ill afford an early two-goal deficit.
Loic Remy was again absent through injury and Adel Taarabt was employed as a solitary striker but it was defensive frailties that caused immediate concerns for Rangers.
Swansea dispelled any suggestion they might be distracted by their League Cup final against Bradford on 24 February by being quicker to the loose ball and far more inventive with their passing.
An unmarked Wayne Routledge played a first-time lay-off to Nathan Dyer, given too much room in the centre of the field, and his shot from distance swerved in front of Cesar who could only push it out. Michu was the first to react, his right-footed volley from an awkward height looping into the net.
Welsh woes for Rangers
QPR have not won at Swansea since a 2-1 victory in the former Division Two in January 1981
Routledge, impressing against his former club, threaded a delightful ball through for Rangel to cut in from the right flank, and after his drive was blocked, the Spaniard coolly converted the rebound with his left foot.
In the early stages the mercurial Taarabt produced an instant touch and flick so sublime it drew applause from both sets of fans but he could not significantly influence the match and demonstrated his frustration by blasting the ball away and tangling with several Swansea players.
Redknapp was also simmering on the touchline and made a double change at the break, which brought immediate success when Taarabt's run and shot from the right was palmed by Michel Vorm into the path of Zamora on the penalty spot and he tapped in clinically.
But two minutes later the visitors found themselves two behind again as Cesar, so impressive in keeping four clean sheets in his past five league games, was beaten by Pablo from close to the byeline following a jinking run and more delightful build-up play.
Rangers pressed again in an absorbingly open encounter and were denied a penalty when a cross from Andros Townsend appeared to strike the arm of Ashley Williams, Kyle Bartley clearing the resulting shot from Stephane Mbia off the line.
Michu, who also scored twice when Swansea beat Rangers 5-0 on the opening day of the season, was then able to hold off the powerful Christopher Samba following an exquisite through ball from Pablo to curl into the corner with his cultured left foot for his 15th league goal of the season.
The Spaniard, troubled in recent weeks by a tight hamstring, was taken off as a precautionary measure with the Wembley showpiece to look forward to, while for QPR, who hit the bar late on through a Shaun Wright-Phillips volley, the visit of Manchester United in a fortnight is rather less inviting.
"This is a big setback for QPR, they capitulated, particularly in an extremely disappointing first 45 minutes.
"They have 12 games to survive in the Premier League and are going to have to play an awful lot better than this if that's to be the case."
Swansea manager Michael Laudrup:
"I was relieved when we scored the third goal but overall it was a great performance.
"We need it right now to get even closer to those 40 points that we want, we're very close now.
"It was really important for me because we know next Sunday Liverpool away at Anfield will be very difficult.
[QPR penalty claims] "From the bench it seemed like a handball and when I came in it still seemed like a handball but a couple of times I have been on the other side of decisions."
QPR boss Harry Redknapp:
"We conceded sloppy goals, I love the way Swansea play but I didn't think they had to work that hard for their goals, they should have been dealt with.
"We looked better in the second half, we got back to 2-1 and I was thinking we'd get something from the game then suddenly we go and give two more goals away.
"If Bobby Zamora was fit for 90 minutes we'd be a different team but he's had a hip injury and he can't play for 90 minutes, he seizes up at half-time. He's what a Premier League player should be, he holds the ball up, brings people into play and he's a target. When he doesn't play we don't have that.
"He needs another operation but that would keep him out for 6-8 months and that's not an option."
Live Text Commentary
Full Time The referee signals the end of the game.90:00 +1:17
Jonathan de Guzman gives away a free kick for an unfair challenge on Armand Traore. Free kick taken by Esteban Granero.90:00 +0:45
Shot by Shaun Wright-Phillips.89:17
Centre by Bobby Zamora, comfortable save by Michel Vorm.89:07
Esteban Granero delivers the ball, clearance made by Kemy Agustien.85:32
Shot by Stephane Mbia. Comfortable save by Michel Vorm.84:04
Andros Townsend crosses the ball, clearance made by Angel Rangel.82:42
Unfair challenge on Stephane Mbia by Sung-Yeung Ki results in a free kick. Stephane Mbia produces a strike on goal direct from the free kick.82:26
Drilled right-footed shot by Stephane Mbia. Jonathan de Guzman gets a block in.81:28
A cross is delivered by Kemy Agustien.79:47 Substitution
Substitution Miguel Michu goes off and Luke Moore comes on.77:52
Free kick awarded for a foul by Clint Hill on Miguel Michu. Free kick taken by Jonathan de Guzman.77:16
Esteban Granero has shot on goal from just outside the box which goes wide of the right-hand upright.75:47
Adel Taarabt has shot on goal from just outside the area which goes wide of the right-hand upright.74:32
Miguel Michu is caught offside. Soares Julio Cesar takes the free kick.71:30
Drilled right-footed shot by Pablo Hernandez. Blocked by Christopher Samba.70:47
Corner from right by-line taken by Jonathan de Guzman.70:12
Corner taken right-footed by Esteban Granero from the right by-line to the near post, Angel Rangel makes a clearance.69:58
Bobby Zamora takes a shot. Blocked by Ashley Williams.68:56
Corner from the right by-line taken by Adel Taarabt, Ashley Williams manages to make a clearance.
Bobby Zamora takes a shot. Blocked by Ben Davies.67:31
Shot by Miguel Michu. Save by Soares Julio Cesar.67:11 Substitution
Substitution Jermaine Jenas goes off and Shaun Wright-Phillips comes on.66:11
The assist for the goal came from Pablo Hernandez.66:11 Goal scored
Goal! - Miguel Michu - Swansea 4 - 1 QPR Miguel Michu grabs a goal from inside the area to the bottom left corner of the goal. Swansea 4-1 QPR.63:08
Andros Townsend takes a shot from deep inside the box clearing the bar.61:41 Substitution
Substitution Wayne Routledge goes off and Kemy Agustien comes on.61:28
A cross is delivered by Miguel Michu, clearance made by Clint Hill.58:44
Effort from deep inside the area by Adel Taarabt misses to the right of the target.56:34
Centre by Andros Townsend. Stephane Mbia takes a shot from 20 yards. Clearance by Kyle Bartley.55:23
Adel Taarabt takes a shot from long distance which goes wide of the right-hand post.54:48
The ball is crossed by Andros Townsend.53:38
Nedum Onuoha concedes a free kick for a foul on Jonathan de Guzman. Jonathan de Guzman restarts play with the free kick.53:23
Wayne Routledge takes a shot. Save by Soares Julio Cesar.51:06
Miguel Michu challenges Stephane Mbia unfairly and gives away a free kick. Free kick taken by Esteban Granero.49:54
Assist on the goal came from Miguel Michu.49:54 Goal scored
Goal! - Pablo Hernandez - Swansea 3 - 1 QPR A goal is scored by Pablo Hernandez from inside the six-yard box to the bottom right corner of the goal. Swansea 3-1 QPR.48:49
Unfair challenge on Nedum Onuoha by Pablo Hernandez results in a free kick. Clint Hill restarts play with the free kick.47:16
Assist on the goal came from Adel Taarabt.47:16 Goal scored
Goal! - Bobby Zamora - Swansea 2 - 1 QPR A goal is scored by Bobby Zamora from close range low into the middle of the goal. Swansea 2-1 QPR.47:08
Adel Taarabt takes a shot. Michel Vorm makes a save.45:56
Foul by Sung-Yeung Ki on Esteban Granero, free kick awarded. Esteban Granero takes the free kick.45:12
Jonathan de Guzman takes a outswinging corner to the near post, Bobby Zamora manages to make a clearance.45:01
The game restarts for the second half.45:01 Substitution
Substitution Shaun Derry goes off and Esteban Granero comes on.45:01 Substitution
Substitution Bobby Zamora replaces Jamie Mackie.45:00 +4:51 Half time
Half Time The referee calls an end to the first half.45:00 +4:22
Nedum Onuoha takes the direct free kick.45:00 +4:22 Booking
Booking Armand Traore goes into the referee's book for unsporting behaviour.45:00 +4:04 Booking
Booking Ben Davies receives a yellow card.45:00 +3:53
Foul by Ben Davies on Nedum Onuoha, free kick awarded.44:15
Pass corner from right by-line crossed in by Jonathan de Guzman, Armand Traore manages to make a clearance.39:57
Kyle Bartley restarts play with the free kick.39:57 Booking
Booking The referee shows Adel Taarabt a yellow card for time wasting.39:50
Adel Taarabt concedes a free kick for a foul on Sung-Yeung Ki.39:15
Pablo Hernandez gives away a free kick for an unfair challenge on Adel Taarabt. Direct free kick taken by Christopher Samba.38:59
Nathan Dyer is ruled offside. Soares Julio Cesar restarts play with the free kick.38:34
The offside flag is raised against Miguel Michu. Indirect free kick taken by Soares Julio Cesar.37:00
Shot from just outside the area by Nathan Dyer goes over the bar.36:43
Jonathan de Guzman produces a cross, Clint Hill manages to make a clearance.36:04
Corner taken by Jonathan de Guzman, save by Soares Julio Cesar.35:43
The ball is sent over by Ben Davies, Miguel Michu takes a shot. Clint Hill gets a block in.29:51
Michel Vorm restarts play with the free kick.29:51 Substitution
Substitution (Swansea) makes a substitution, with Kyle Bartley coming on for Chico.29:51
Chico fouled by Stephane Mbia, the ref awards a free kick.29:09
Sung-Yeung Ki concedes a free kick for a foul on Stephane Mbia. Adel Taarabt restarts play with the free kick.28:13
Centre by Angel Rangel, clearance by Christopher Samba.26:38
Ben Davies concedes a free kick for a foul on Andros Townsend. Adel Taarabt takes the free kick.24:01
Free kick awarded for an unfair challenge on Clint Hill by Pablo Hernandez. Free kick taken by Clint Hill.23:24
Free kick awarded for an unfair challenge on Jonathan de Guzman by Jermaine Jenas. Free kick taken by Chico.22:00
Foul by Andros Townsend on Ben Davies, free kick awarded. Michel Vorm takes the direct free kick.20:13
A cross is delivered by Ben Davies, Armand Traore makes a clearance.17:43
The assist for the goal came from Wayne Routledge.17:43 Goal scored
Goal! - Angel Rangel - Swansea 2 - 0 QPR A goal is scored by Angel Rangel from close in to the bottom left corner of the goal. Swansea 2-0 QPR.17:43
Angel Rangel takes a shot. Save by Soares Julio Cesar.16:02
Centre by Andros Townsend, Clint Hill makes a clearance.14:17
Free kick awarded for a foul by Shaun Derry on Nathan Dyer. Free kick taken by Jonathan de Guzman.13:16
Miguel Michu takes a shot. Soares Julio Cesar makes a save.11:55
Wayne Routledge fouled by Stephane Mbia, the ref awards a free kick. Free kick taken by Jonathan de Guzman.9:39
Strike comes in from Jonathan de Guzman from the free kick.9:39 Booking
Booking Christopher Samba goes into the referee's book.9:33
Christopher Samba challenges Miguel Michu unfairly and gives away a free kick.7:42
Assist on the goal came from Nathan Dyer.7:42 Goal scored
Goal! - Miguel Michu - Swansea 1 - 0 QPR Goal scored by Miguel Michu from inside the six-yard box to the bottom right corner of the goal. Swansea 1-0 QPR.7:42
Nathan Dyer takes a shot from 20 yards. Save made by Soares Julio Cesar.2:01
Outswinging corner taken by Jonathan de Guzman, clearance made by Christopher Samba.0:00
The referee gets the match started.
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