The Portuguese coach's side got off to a fine start at Stamford Bridge, but Diego Simeone's men showed class to turn the tie around and book a final against Real Madrid.
The visitors came from behind to reach their first final in Europe's premier club competition for 40 years and keep alive their hopes of a Champions League and La Liga double.
A cagey first leg of the semifinal tie last week finished goalless, but former Atletico captain Fernando Torres put Chelsea in front Wednesday - and was emotional as his teammates celebrated - against his boyhood club, only for Adrian Lopez to equalize just before halftime.
Atletico took that momentum into the second half and Diego Costa - a reported Chelsea target - put it in front from the penalty spot with his 36th goal of the season after substitute Samuel Eto'o brought him down in his first involvement in the game.
|VIEW FROM STAMFORD BRIDGE
|By Greg Stobart
A fourth Champions League semifinal defeat in a row for Jose Mourinho, but the Chelsea manager will surely have no complaints this time. His side was totally outclassed here by Atletico Madrid, which played with great speed, quality and was ruthless in front of goal.
Chelsea took the lead through Fernando Torres’ deflected strike in the first half, but Mourinho’s game plan appeared to fall apart after some shocking defending allowed Adrian to steer in the equalizer just before halftime. After the break, the La Liga leaders played with breathtaking speed and sealed the semifinal through goals from Diego Costa and Arda Turan.
Chelsea huffed and puffed, and it might have scored if it wasn’t for its own loanee Thibaut Courtois in the Atletico goal, but in the final 20 minutes there seemed to be an acceptance that the team had simply been outclassed.
Arda Turan sealed Atletico's progress into what will be a first final - to take place May 24 at Estadio da Luz - in the competition between two sides from the same city and ensure Jose Mourinho misses out on a showdown with his former club.
The Portuguese's wait to become the first manager to win the famous trophy for three different clubs continues, and he will have to hope his side wins the Premier League to avoid a trophyless first season back in London.
Mourinho was able to name fit-again captain John Terry (ankle) and Eden Hazard (calf) in his starting lineup, while former Chelsea midfielder Tiago replaced the suspended Gabi and also skippered the Atletico side.
Koke's cross-shot almost caught Mark Schwarzer out in the early exchanges, though Chelsea replied through David Luiz's audacious overhead kick, which flew narrowly wide.
The breakthrough finally came nine minutes before halftime as Willian displayed fine close control on the right before Cesar Azpilicueta cut the ball back for the onrushing Torres and his right-footed strike found the net via a slight deflection.
Torres refused to celebrate out of respect for his former club, but Atletico was euphoric a minute before halftime when Adrian capitalized on some hesitant defending to equalize with a scuffed right-footed effort from Juanfran’s cross.
Terry was next to go close at the other end, but Thibaut Courtois' razor-sharp reflexes denied his parent club.
Mourinho replaced Ashley Cole with Eto'o nine minutes before the break - and he must have been ruing that decision soon after when the Cameroon striker upended Costa and referee Nicola Rizzoli awarded a penalty.
Costa was booked for time wasting as he struggled to get the ball to stay on the spot but held his nerve to fire the ball into the roof of the net as Schwarzer went the wrong way.
There was no let up in the action, and Luiz got on the end of Willian's inviting free kick with a powerful header which struck the crossbar - Courtois somehow diverting the rebound over.
But any hopes of a Chelsea fightback were ended by Turan, who calmly tucked the ball into an empty net when the ball came back nicely for him after Schwarzer had tipped his powerful header against the bar 18 minutes from time.
Both Atletico and Real could enter the final as Spanish champions. Simeone's side will be seeking a first top European crown, with its local rivals out to clinch La Decima.