Atletico Madrid booked their place in the Champions League final to face their cross-town rivals with a stunning result at Stamford Bridge.
José Mourinho's men set up to defend against the visitors, but some individual errors proved costly and Atleti deservedly got the goals to make an historic final for the club.
Minutes after Fernando Torres had fired the hosts ahead against his former club, some poor defending allowed Adrian Lopez to equalise, before Samuel Eto'o conceded a penalty in the second half which Costa converted.
Luiz almost gave Chelsea a route back into the game when he struck the post afterwards, but Arda Turan finished the hosts off with a third goal to complete their demise.
In the remaining time, Atletico cruised to a deserved victory, revealing their quality to the world in having shown up at Stamford Bridge and thoroughly outplayed Chelsea.
Mourinho will surely point to the rebuilding work to be done - his side looked a long, long way from being the best side in Europe, and even his tactical mastery could take them no further.
36' - TORRES GOAL! (Chelsea 1-0 Atletico): Chelsea take the lead in the tie as Fernando Torres scores against his old club, finding the net through a huge deflection off Mario Suarez.
44' - ADRIAN GOAL! (Chelsea 1-1 Atletico): Chelsea's gameplan comes undone as some woeful defending allows Juanfran to hook the ball back across goal for Adrian Lopez to smash home, leaving the hosts chasing the game.
60' - COSTA PENALTY! (Chelsea 1-2 Atletico): Samuel Eto'o had only been on the pitch for a couple of minutes when he gave away a cheap penalty, bringing down Diego Costa in the area. The big striker stepped up to blast his penalty home and leave Chelsea needing two goals to progress.
72' - TURAN GOAL! (Chelsea 1-3 Atletico): The knockout blow to Chelsea, and unforgivably, they fall for the same trick twice as Juanfran provides exactly the same assist for the first goal for Arda Turan.
TALKING POINT - Right to defend? All the talk of the morality and ethics of dour, negative football has perhaps obscured the reality for this game - was José Mourinho correct to pick such a negative lineup? Atletico seemed much more emboldened to get numbers forward than in the first leg, and although poor defending aided their attacking prowess, Chelsea had far more threats to keep track of than their opponents and it ended up costing them.
Mark Schwarzer was the oldest man to start a Champions League knockout game after he played in goal in the absence of Petr Cech for Chelsea tonight.
Diego Costa's penalty means that he now has 8 goals in 8 games in this season's Champions League.
MAN OF THE MATCH
Adrian Lopez: Chelsea fans wishing to clutch at straws may point to the fact that he could have had two yellow cards before being withdrawn, but the drifting of the Atletico frontman was key to his team's attacking prowess tonight. A more subtle option than Costa, he was better suited to exploit a Chelsea defence which stuck rigidly to the basics.
Chelsea: Schwarzer 5, Cole 4, Terry 5, Cahill 6, Ivanovic 6, Azpilicueta 7, Ramires 6, Luiz 7, Willian 7, Hazard 6, Torres 6. Subs: Eto'o 4, Ba 6, Schurrle 6.
Atletico Madrid: Courtois 7, Juanfran 8, Miranda 7, Godin 7, Filipe 7, Koke 6, Tiago 7, Suarez 6, Turan 7, Costa 6, Adrian 8.