Chelsea huffed and puffed but could not break the Swansea house down as the Welsh side stormed into the final of the Capital One Cup with a 2-0 aggregate victory.
Eden Hazard was sent off late on in the second half in the most bizarre of circumstances as the Blues self-destructed in a goalless draw, allowing Swansea to book a Wembley berth with League Two side Bradford City lying in wait in the final.
Swansea began, happy to let Chelsea have the bulk of the possession, looking to spring quickly on the counter-attack. The onus was very much on Chelsea's triumvirate of playmakers - Juan Mata, Oscar and Hazard - to create the opening for Demba Ba, preferred for Fernando Torres up front.
Ba thought he had won his side an early penalty, but clearly went down too easily inside the box, leaning into the challenge of Ben Davies - referee Chris Foy gave a good talking to to the Chelsea striker, but there was no yellow card.
Swansea nearly put the tie to bed immediately at the other end, but Cesar Azplicueta brilliantly blocked a Wayne Routledge goal-bound effort off a cross from Jonathan De Guzman.
Michu then almost crowned his new four-year contract with a typical low left-footed drove across the goalkeeper, off a through ball from Routledge, which Petr Cech did well to save.
Chelsea defender Gary Cahill thought he had scored, but saw his looping header off a corner cleared off the line by Angel Rangel, with Ramires seeing his well-struck long-range effort, well held by goalkeeper Gerhard Tremmel soon after.
Chelsea's trio of midfielders behind Ba nearly broke through after a string of passes allowed Oscar to sneak into the box, but the ball was taken away from the Brazilian at the crucial moment, as the Blues were left frustrated.
Ba then nearly scored the opener on the stroke of halftime, but his swivel and shot went just over the crossbar.
Chelsea, knowing they needed to take the game to Swansea in the final 45 minutes, started to press and press the Swansea defense, which kept holding firm in the opening 20 minutes of the second half. The home crowd started to grow a little anxious with all the Blues possession, and also knowing they were getting closer and closer to an historic Wembley final.
As time wore on, Chelsea got more and more desperate and the weight of finding at least that opening goal was increasingly falling upon the Blues' best player this season Mata.
The little Spaniard nearly provided that relief, but saw his dipping, swerving shot just about kept out by Tremmel, much to the away side's frustration.
Chelsea manager Rafa Benitez brought on David Luiz for Branislav Ivanovic, but chose not to use Torres and employ two strikers up front.
Just when it looked like things couldn't get any worse for Chelsea, it did. In the most bizarre of sending-offs you will ever see, Hazard was shown a straight red card for kicking out at a ball boy - yes a ball boy! - who refused to give the ball to the Chelsea playmaker.
Torres finally came on in the final ten minutes, but really it was too little too late for the ten-men of Chelsea to make a dent in the tie, as Swansea celebrated a thoroughly deserved trip to Wembley, and with it a chance to make history.