The Swans took another step towards a first ever major final after beating the Champions of Europe Chelsea 2-0 in the Capital One Cup semi-final first leg.
Michael Laudrup's side put in a superb defensive effort, for they were forced to deal with heavy pressure applied by the Blues, but goals from Michu and substitute Danny Graham gave the Swans a healthy advantage for the return leg at the Liberty.
Michu curled home his 16th goal of the season in the 39th minute after he was set up by Jonathan de Guzman after the midfielder had pinched possession off Branoslav Ivanovic.
A stern performance defensively, and some excellent stops by Gerhard Tremmel, ensured Chelsea were kept out, and things got even better for the visitors in added-on time.
Graham pounced on a pass back from Ivanovic, and the striker rounded keeper Ross Turnbull before slotting home and celebrating in front of the Jack Army.
New signing Demba Ba thought he had pulled one back a minute later for the FA Cup holders, only to be denied by the offside flag.
It meant the Swans not only claimed yet another historic victory, but they take a 2-0 advantage back to the Liberty for the return leg on Wednesday, January 23, in what is sure to prove another thrilling, tense night in South West Wales.
Michael Laudrup made five changes. As promised, the Great Dane brought Gerhard Tremmel back into the fold, with the German keeper having been used in every game in the competition so far.
Ashley Williams returned to the heart of defence to lead the side as Garry Monk dropped to the bench, while Angel Rangel was fit again after a slight hamstring concern and started in place of Dwight Tiendalli.
Club record signing Pablo Hernandez returned to a ground where he featured in the Champions League for Valencia just over a year ago, while top-scorer Michu got the nod up front ahead of Danny Graham.
Rafa Benitez was without captain John Terry, so Ashley Cole led the Blues from left-back. Also missing were John Obi Mikel, Victor Moses and keeper Petr Cech, which meant Ross Turnbull was between the sticks.
Frank Lampard, a former Swans loanee at the start of his career, was among the substitutes bench which also included recent signing Demba Ba from Newcastle.
Chelsea: Ross Turnbull, Branislav Ivanovic, Ashley Cole (capt), David Luiz, Ramires (Frank Lampard, 71), Fernando Torres (Demba Ba, 82), Juan Mata, Oscar (Marko Marin, 83), Eden Hazard, Gary Cahill, Cesar Azpilicueta.
Subs: Hilario, Paulo Ferreira, Ryan Bertrand, Nathan Ake.
Swans: Gerhard Tremmel, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton, Ki Sung Yueng, Jonathan de Guzman, Pablo Hernandez, Wayne Routledge (Dwight Tiendalli, 63), Michu (Danny Graham, 83).
Subs: Michel Vorm, Garry Monk, Kemy Agustien, Nathan Dyer, Itay Shechter.
The hosts made the brighter start, with Branislav Ivanovic heading over from a Juan Mata corner before Fernando Torres fired high and wide from 20 yards.
Chelsea then created their best chance after ten minutes, Oscar and Mata linking to set up Ramires on the edge of the box, and the midfielder's initial dummy shot bought him time to turn back inside, but his weak show was easily saved by Gerhard Tremmel.
The Swans first threatened after 20 minutes, with Michu's 20-yard effort being parried by Ross Turnbull before the keeper collected.
Chelsea responded instantly at the other end, Cesar Azpilicueta doing well to win possession off Wayne Routledge before shooting just wide of the far post with Tremmel untroubled.
Gary Cahill then rose highest to meet Oscar's corner, but the English centre-back's header was off target, while Mata wasted a glorious chance to open the scoring after Eden Hazard's fine play, but Mata's feeble strike was collected by Tremmel.
Mata probed again, but saw his low drive bounce wide of the far post after a fine flick from Oscar, and then the Spaniard was just beating to Fernando Torres' through pass by Tremmel after the Swans had lost possession near the halfway line.
Then, out of nowhere, the Swans took the lead after 39 minutes. After Turnbull passed short to Ivanovic, the defender lost control and was robbed of possession by Jonathan de Guzman, and when he touched on for Michu, the Spaniard curled a sublime effort past the keeper.
Chelsea looked for an instant response, and Ivanovic went close to amending for his error minutes later but his powerful curling shot was palmed out by the diving Tremmel, who produced a superb save.
Half-time: Chelsea 0 Swans 1
Chelsea enjoyed the vast majority of possession and territory in the early stages of the half, but it was the Swans who went closest as Michu volleyed over after connecting with Wayne Routledge's cross.
David Luiz then saw his 30-yard free-kick drop just inches wide with Tremmel at full stretch before he was denied again by the German keeper after a thunderous strike from ten yards.
Laudrup then made his first change with just under 30 minutes to go as Dwight Tiendalli replaced Routledge, meaning Angel Rangel moved to the right-back and the Dutchman slotting in at full-back.
Rafa Benitez did the same shortly after, Frank Lampard coming on in place of Ramires as the hosts looked to get back on level terms.
The Swans continued to plug away, and Ki almost sent Michu in on goal, but the offside flag was raised to deny him.
More changes followed for the hosts as Demba Ba came on for his home debut in place of Torres in the 81st minute while Marko Marin replaced Oscar.
Laudrup also made a switch, Danny Graham coming on in place of scorer Michu, with the Swans looking to hold on for the remaining seven minutes.
It was to prove a tense affair, Ba rising highest to meet Ivanovic's cross only to head straight at Tremmel before the striker met another cross only to steer it wide.
Ba was at the heart of the next big call, Ben Davies' sliced clearance heading back towards goal, and when the striker when down under Tremmel's challenge, referee Anthony Taylor booked the striker for simulation.
It proved an important call, as just seconds later - in the first of three added minutes - another major error from Ivanovic cost the hosts dearly.
The Serb passed back to keeper Turnbull under no pressure, but Graham was lurking and when he rounded the keeper he slotted home despite the desperate efforts of Luiz to deny him.
It was the stuff of dreams for the Jack Army, who were still celebrating when, at the other end, Ba steered his effort past the excellent Tremmel only to be denied by the offside flag.
Tense a finish it was, the Swans could celebrate at the final whistle.
But with this only being half-time in the two-leg affair, it promises to be a thrilling night back at the Liberty.