Gylfi Sigurdsson fired the Swans to their first-ever Barclays Premier League victory over Chelsea at the Liberty Stadium.
The Icelandic midfielder fired home his 11th goal of the season in the first half to secure a thoroughly deserved 1-0 win for the home side.
Francesco Guidolin’s side were the dominant side throughout the first-half, and after Sigurdsson’s 25th-minute opener - a well-struck volley past Asmir Begovic - the home side had a string of opportunities to extend their advantage.
Leroy Fer was unfortunate to see a close-range effort bundled clear by the Chelsea defence, while the impressive Jefferson Montero headed just over the bar in the second half with the goal gaping.
Lukasz Fabianski, meanwhile, had little to do in way of saves to make, with Alexandre Pato going closest to equalising for the visitors with a flicked effort, which narrowly evaded the far post.
The crucial three points means the Swans move up to 12th position in the Premier League and onto 40 points.
The Swans make four changes to the starting XI for the Barclays Premier League fixture with defending champions Chelsea at the Liberty (3pm).
From the side that came back to draw 2-2 at Stoke City last time out, Andre Ayew returns to action after recovering from an ankle injury that sidelined him for three games.
Neil Taylor returns to Francesco Guidolin's starting plans as he gets the nod at left-back after coming off the bench at the Britannia, while Jefferson Montero makes his first league start since the Boxing Day win over West Brom.
The final change sees Italian striker Alberto Paloschi lead the line as he is rewarded for scoring the equaliser against the Potters, while Modou Barrow is among the substitutes after missing the trip to Stoke.
Leon Britton, however, is ruled out with a back problem.
Chelsea - unbeaten in their last 15 games - are without suspended striker Diego Costa, Loic Remy (groin), John Terry (Achilles), Eden Hazard (groin) and Nemanja Matic (leg).
Lukasz Fabianski, Angel Rangel, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Jack Cork, Leroy Fer, Gylfi Sigurdsson, Andre Ayew (Wayne Routledge, 67), Jefferson Montero (Kyle Naughton, 84), Alberto Paloschi (Bafe Gomis, 75).
Kristoffer Nordfeldt, Jordi Amat, Ki Sung-Yueng, Modou Barrow.
Asmir Begovic, Branislav Ivanovic (capt), Cesc Fabregas, Baba Rahman, Oscar, Alexandre Pato (Bertrand Traore, 64), John Obi Mikel, Pedro, Matt Miazga (Kenedy, HT), Cesar Azpilicueta, Ruben Loftus-Cheek (Falcao, 76).
Thibaut Courtois, Kasey Palmer, Ola Aina, Charlie Colkett.
The last time these two sides met at the Liberty, it ended in a 5-0 rout in favour of the Blues, but Swansea started this afternoon as if that defeat was nothing but a distant memory.
The visitors were slow out of the blocks, while the Swans started brightly, controlling possession and dictating play from the first whistle.
But it took until the 17th minute for the game to see its first chance on goal as Asmir Begovic produced a fine save to deny Gylfi Sigurdsson his 11th goal of the season.
After Swansea’s pressing forced Matt Miazga into gifting possession to the lively Jefferson Montero, the Ecuadorian winger threaded through for Sigurdsson, whose strike was pushed away by Begovic.
The home side then had an even greater chance to open the scoring when Angel Rangel burst through on goal, only to drag his effort wide of the target, much to the relief of Chelsea’s Bosnian goalkeeper.
But the Swans were rewarded for their impressive start to the afternoon when Sigurdsson volleyed home in the 25th minute.
Montero’s inviting cross into the box was cleared only as far as the Icelandic midfielder, whose first-time strike nestled into the bottom corner.
Montero, who played a huge role in Swansea’s opener, was causing Chelsea full-back Cesar Azpilicueta problems down the left flank and the home side’s chances for a second goal were beginning to pile up.
Ten minutes before the interval, the ball fell to Leroy Fer inside the Swans box, but his goal-bound effort couldn’t make its way through a body of blue shirts.
Andre Ayew was then nearly provided a present from Begovic, whose miscued clearance landed at the Ghanaian’s feet, only for Ayew to send the ball straight back at the Chelsea stopper.
On the cusp of half-time Alexandre Pato wasted a glorious chance to equalise for the visitors when the ball fell loose to him inside the Swans box, but he made a hash of his first-time effort, sending the ball well wide of the target.
HALF-TIME: Swans 1-0 Chelsea
The Swans began the second half as they left off as neat link-up play between Sigurdsson and Montero provided Alberto Paloschi with a chance to make it 2-0, but the Italian’s first touch was heavy, allowing Begovic to quell the danger.
At the other end, meanwhile, Pato saw a goal chalked off for offside before seeing a clever flick from Pedro’s low cross trickle narrowly past the far post.
As the hour-mark approached, Jack Cork saw a thunderous effort from 25 yards spectacularly saved by Begovic, before Sigurdsson’s attempt double his and Swansea’s tally blocked by last-ditch challenge by John Obi Mikel.
Sigurdsson then turned provider after skipping past Baba Rahman, teeing up Montero inside the six-yard box. But with the goal gaping, the Iceland international’s cross was slightly too high for Montero, who headed just over the bar.
Time was running out for Chelsea to snatch an equaliser. Blues boss Guus Hiddink introduced Falcao in place of Pato, in an effort to snatch a late leveller.
The Colombian striker threatened with a deflected effort, but Lukasz Fabianski was on hand to make a comfortable save with five minutes left on the clock.
On the cusp of the final whistle, substitute Kyle Naughton had an opportunity to finish the job for the hosts when Bafe Gomis cut back for the full-back, but his effort was blocked by Rahman.