Swansea won at Chelsea for the first time in 87 years to head into the Capital One Cup semi-final second leg with a precious two-goal advantage.
The hosts dominated in the first half but an error from defender Branislav Ivanovic allowed Michu to curl home.
The home side continued to press but Ivanovic was again at fault in stoppage time when Danny Graham seized on his poor backpass to seal the win.
Graeme Le SauxFormer Chelsea defender
"If you look at Bradford and Swansea they both had a plan and were highly disciplined. Swansea really deserve to come away from this game with something. Michael Laudrup has communicated his plan, got his players focused and Michu stands out in sacrificing his creativity to do a job and they all worked very hard together. Chelsea are relying too much on the individual players rather than a collective plan but I would have expected them to have scored a couple of goals from the chances they had."
Demba Ba thought he had snatched a late goal only for it to be ruled offside.
The win puts Swansea firmly in command heading into the second leg at the Liberty Stadium on 23 January as they look to end a 100-year wait for a first major trophy.
Chelsea, though, were the architects of their own downfall.
They enjoyed plenty of possession throughout the encounter but were let down by poor decision-making in the final third.
The home side spent the initial exchanges patiently passing the ball around as they probed for potential openings in the Swansea backline.
They were nearly rewarded in the 11th minute when Oscar and Eden Hazard combined to unlock the Swansea defence and present Ramires with a chance on goal, but the midfielder's toe-poked effort lacked power and was comfortably saved by keeper Gerhard Tremmel.
That early chance was not a sign of things to come, however, as play once again settled into a pedestrian pace, although Chelsea continued to dominate.
'Fantastic' Swansea delight Laudrup
The home side did not trouble Tremmel again until the 26th minute when Hazard surged into the Swansea area before squaring a pass for the unmarked Juan Mata, but the Spaniard's low shot was gratefully scooped up by Tremmel.
By now Chelsea were looking a confident side and Mata almost made amends for failing to make the most of that opportunity minutes later when he raced onto Oscar's smart back-heel but his shot trickled agonisingly wide of the far post.
It seemed only a matter of time before Chelsea would take the lead but poor defending instead saw Swansea snatch the opener six minutes before the break.
Ivanovic dithered with the ball just outside his own area and Jonathan de Guzman took full advantage, stealing possession before immediately passing to Michu and the in-form striker's curled effort flew beyond Ross Turnbull, taking his total for the season to 16.
Michu was clearly a player brimming with confidence and he attempted an audacious overhead kick early in the second half, but the ball sailed harmlessly over Turnbull's goal.
Ba goal not offside - Benitez
Tremmel maintained his side's slender advantage just before the hour when Hazard rolled the ball across the edge of the area for Luiz but his well-struck effort was kept out by the Swansea keeper.
The visitors were clearly content to try and protect their lead, much to the frustration of the home side, who continued to try and carve out an opening.
Frank Lampard replaced Ramires with 20 minutes remaining, before Ba was introduced 10 minutes later, replacing Fernando Torres as Chelsea interim manager Rafael Benitez looked to reinvigorate his attack.
Ba quickly made his presence known and felt he should have had a penalty as the game entered stoppage time after clashing with Tremmel when challenging for possession, but instead he was booked for diving.
Any hopes of Chelsea snatching an equaliser were ended shortly after as Ivanovic's poor backpass allowed substitute Graham to run in, round the keeper and fire into the empty net.
Chelsea thought they had snatched what would have been a potentially important late goal when Ba powered a shot into the net from Lampard's knock on, but the striker had strayed just offside.
90:00+4:07 The game is over, as the referee blows his whistle.
90:00+2:25 Demba Ba is caught offside. Gerhard Tremmel takes the indirect free kick.
90:00+1:05 GOAL - Danny Graham:Chelsea 0 - 2 Swansea Danny Graham fires in a goal from inside the penalty area low into the middle of the goal. Chelsea 0-2 Swansea.
90:00+0:38 Gerhard Tremmel takes the direct free kick.
90:00+0:38 Booking Demba Ba booked for unsporting behaviour.
90:00+0:09 Foul by Demba Ba on Gerhard Tremmel, free kick awarded.
89:27 Shot from outside the penalty box by Cesar Azpilicueta goes wide right of the goal.
89:16 Eden Hazard sends in a cross, clearance made by Pablo Hernandez.
88:05 The ball is swung over by Ashley Cole, clearance made by Ben Davies.
86:40 Centre by Marko Marin, Headed effort from deep inside the area by Demba Ba misses to the left of the goal.
86:17 Branislav Ivanovic fouled by Angel Rangel, the ref awards a free kick. Branislav Ivanovic takes the direct free kick.
85:44 The ball is crossed by Branislav Ivanovic, Demba Ba takes a shot. Save by Gerhard Tremmel.
85:23 Juan Mata fouled by Dwight Tiendalli, the ref awards a free kick. Juan Mata takes the direct free kick.
84:29 Shot on goal by David Luiz from long range goes harmlessly over the target.
83:29 Danny Graham gives away a free kick for an unfair challenge on Ashley Cole. Direct free kick taken by Ashley Cole.
82:12 Substitution Danny Graham on for Miguel Michu.
82:12 Substitution Emboaba Oscar goes off and Marko Marin comes on.
81:27 Drilled right-footed shot by Frank Lampard. Gerhard Tremmel makes a comfortable save.
80:51 Angel Rangel is flagged offside by the assistant referee. Gary Cahill takes the free kick.
80:21 Substitution Demba Ba is brought on as a substitute for Fernando Torres.
80:09 Eden Hazard crosses the ball.
79:25 A cross is delivered by Cesar Azpilicueta, clearance made by Ashley Williams.
76:11 Miguel Michu is caught offside. Indirect free kick taken by Ross Turnbull.
75:38 Emboaba Oscar delivers the ball, save by Gerhard Tremmel.
75:24 Foul by Sung-Yeung Ki on Eden Hazard, free kick awarded. Juan Mata restarts play with the free kick.
72:02 Eden Hazard gives away a free kick for an unfair challenge on Chico. The ball is delivered by Jonathan de Guzman, Shot by
Ashley Williams. Comfortable save by Ross Turnbull.
71:08 Unfair challenge on Miguel Michu by Branislav Ivanovic results in a free kick. Free kick crossed right-footed by Jonathan
de Guzman, David Luiz makes a clearance.
70:15 Substitution Frank Lampard on for Nascimento Ramires.
69:50 The ball is swung over by David Luiz, clearance made by Ashley Williams.
69:15 Emboaba Oscar crosses the ball, Pablo Hernandez gets a block in.
67:20 Eden Hazard fouled by Ben Davies, the ref awards a free kick. The free kick is delivered left-footed by Juan Mata from right
66:37 Nascimento Ramires has a mishit shot. Blocked by Sung-Yeung Ki.
66:22 Inswinging corner taken from the right by-line by Juan Mata, clearance by Chico.
66:10 Cesar Azpilicueta produces a cross, blocked by Ben Davies.
65:47 Miguel Michu is caught offside. Free kick taken by Gary Cahill.
63:37 Foul by Miguel Michu on Nascimento Ramires, free kick awarded. David Luiz takes the direct free kick.
63:04 Unfair challenge on Sung-Yeung Ki by Nascimento Ramires results in a free kick. Direct free kick taken by Sung-Yeung Ki.
61:59 Substitution Wayne Routledge goes off and Dwight Tiendalli comes on.
60:57 Corner taken right-footed by Juan Mata, save by Gerhard Tremmel.
60:35 Cesar Azpilicueta crosses the ball, blocked by Ben Davies.
57:52 Shot by David Luiz. Save made by Gerhard Tremmel.
56:52 Centre by Fernando Torres, comfortable save by Gerhard Tremmel.
56:42 The ball is delivered by Fernando Torres, Chico manages to make a clearance.
54:51 Unfair challenge on David Luiz by Jonathan de Guzman results in a free kick. Strike comes in from David Luiz from the free
53:08 The ball is delivered by Wayne Routledge, Effort on goal by Miguel Michu from inside the area goes harmlessly over the bar.
51:42 Shot from just outside the area by Eden Hazard misses to the left of the target.
51:04 Cesar Azpilicueta produces a cross, Gerhard Tremmel makes a comfortable save.
50:09 Ashley Cole sends in a cross.
49:16 Miguel Michu is caught offside. Gary Cahill takes the indirect free kick.
47:25 Shot comes in from David Luiz from the free kick.
47:25 Booking Chico goes into the book for unsporting behaviour.
47:19 Chico challenges Fernando Torres unfairly and gives away a free kick.
46:24 Eden Hazard fouled by Angel Rangel, the ref awards a free kick. David Luiz takes the direct free kick.
45:49 The official flags Fernando Torres offside. Chico takes the free kick.
45:01 The second half kicks off.
45:00+1:27 The match has reached half-time.
45:00+1:13 The ball is delivered by David Luiz, clearance made by Angel Rangel.
45:00+0:21 Foul by Jonathan de Guzman on Branislav Ivanovic, free kick awarded. Juan Mata crosses the ball in from the free kick.
44:38 Sung-Yeung Ki challenges Nascimento Ramires unfairly and gives away a free kick. Gary Cahill takes the free kick.
43:48 Cesar Azpilicueta produces a right-footed shot from just outside the box that goes wide right of the target.
42:28 Inswinging corner taken left-footed by Juan Mata from the right by-line to the near post, Fernando Torres produces a header
from deep inside the six-yard box which goes wide of the right-hand post.
42:08 Curled right-footed shot by Branislav Ivanovic. Save made by Gerhard Tremmel.
41:25 Direct free kick taken by Juan Mata.
41:25 Booking The referee shows Pablo Hernandez a yellow card for unsporting behaviour.
40:55 Emboaba Oscar fouled by Pablo Hernandez, the ref awards a free kick.
38:05 The assist for the goal came from Jonathan de Guzman.
38:05 GOAL - Miguel Michu:Chelsea 0 - 1 Swansea Miguel Michu finds the back of the net with a goal from the edge of the penalty box to the top left corner of the goal. Chelsea
36:33 Effort from outside the box by David Luiz goes wide right of the target.
36:17 Emboaba Oscar crosses the ball, clearance by Ashley Williams.
31:52 The offside flag is raised against Miguel Michu. Gary Cahill takes the free kick.
31:34 Fernando Torres delivers the ball, Gerhard Tremmel makes a comfortable save.
30:57 Leon Britton fouled by Nascimento Ramires, the ref awards a free kick. Leon Britton takes the free kick.
30:26 Shot by Juan Mata from deep inside the penalty area misses wide to the left of the target.
25:50 Juan Mata has an effort at goal from 12 yards. Save made by Gerhard Tremmel.
24:52 Outswinging corner taken from the right by-line by Emboaba Oscar, Header from deep inside the area by Gary Cahill goes over
24:39 The ball is sent over by Juan Mata, clearance by Ben Davies.
23:20 Long range shot by Gary Cahill goes wide right of the goal.
22:48 Cesar Azpilicueta has an effort at goal from outside the area which misses left.
22:22 Juan Mata takes a shot. Blocked by Ben Davies.
20:54 Miguel Michu takes a shot. Save made by Ross Turnbull.
20:38 Wayne Routledge delivers the ball, David Luiz manages to make a clearance.
19:41 Cesar Azpilicueta concedes a free kick for a foul on Ben Davies. Direct free kick taken by Leon Britton.
18:55 Fernando Torres is ruled offside. Ashley Williams takes the indirect free kick.
17:07 A cross is delivered by Wayne Routledge, save made by Ross Turnbull.
16:13 Juan Mata delivers the ball, clearance by Angel Rangel.
15:25 Cesar Azpilicueta produces a cross, Ashley Williams manages to make a clearance.
12:39 The referee blows for offside. Ashley Cole takes the indirect free kick.
10:25 Nascimento Ramires takes a shot. Comfortable save by Gerhard Tremmel.
8:45 Fernando Torres produces a right-footed shot from just outside the box that misses to the right of the net.
7:51 Inswinging corner taken by Eden Hazard from the left by-line, Fernando Torres takes a shot.
7:32 Centre by Ashley Cole, blocked by Chico.
6:47 Fernando Torres crosses the ball, Branislav Ivanovic produces a header from inside the area that goes over the bar.
6:28 Corner taken left-footed by Juan Mata.
6:17 Emboaba Oscar delivers the ball, clearance by Ashley Williams.
4:14 Jonathan de Guzman fouled by Nascimento Ramires, the ref awards a free kick. Pablo Hernandez takes the direct free kick.
1:37 Sung-Yeung Ki challenges Emboaba Oscar unfairly and gives away a free kick. Direct free kick taken by Juan Mata.
0:51 David Luiz challenges Leon Britton unfairly and gives away a free kick. Chico takes the direct free kick.
0:00 The ref blows the whistle to start the match.
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