Atletico Madrid set up a UEFA Champions League final against city rivals Real Madrid after coming from behind to win 3-1 at Chelsea last Wednesday.
After a 0-0 draw in the first leg of their semi-final, former Atletico striker Fernando Torres put the Blues ahead in the 36th minute at Stamford Bridge, but the London club were to lead the tie for only eight minutes.
Adrian Lopez scrambled home an equaliser shortly before the break and second-half goals by Diego Costa, from the penalty spot, and Arda Turan sealed Atletico's place in the final of Europe's biggest club competition for the first time since 1974.
Diego Simeone's team are also two wins from claiming a first Spanish La Liga title in 18 years, meaning that they could be looking to complete an improbable double when they meet their old foes Real in Lisbon on 24 May.
Chelsea manager Jose Mourinho, meanwhile, was denied a reunion with his former employers Real, with whom he had also experienced semi-final disappointment in each of the previous three seasons.
Fears of a new-fangled defensive configuration by Chelsea proved unfounded, as Cesar Azpilicueta was deployed as a fairly orthodox right-sided midfielder, but the early stages proved every bit as cagey as last week's first leg.
Koke almost gave Atletico a fourth-minute lead with a mishit left-wing cross that deceived Mark Schwarzer and hit the crossbar, but the teams were generally content to hold each other at arm's length.
The tie was on a knife-edge, but nine minutes from half-time Chelsea seized the initiative. After Willian ran into a blind alley on the right flank, Azpilicueta followed up with a low cross that Torres steered past Thibaut Courtois via a deflection off Mario Suarez for the opening goal.
Stamford Bridge celebrated in anticipation of a bountiful harvest. It was the first goal that Atletico had conceded in seven games, but within the blink of an eye they were in control of the tie.
Former Chelsea midfielder Tiago Mendes picked out right-back Juanfran with a floated pass to the back post, and his volleyed cross bobbled between a phalanx of defenders to Adrian, who swept home.
Despite Chelsea's need for goals, it was Atletico who began the second half on top, with Schwarzer brilliantly tipping over a Turan half-volley and then comfortably fielding a low effort from Tiago.
In response, John Terry saw a header sharply blocked by Courtois, who is on loan at Atletico from Chelsea, before Mourinho sent on Samuel Eto'o in place of Ashley Cole.
Referee Nicola Rizzoli had already ignored an Atletico penalty claim when Turan was bundled over by Azpilicueta, but when Costa went down after skilfully nicking the ball past Eto'o, the Italian awarded a spot-kick.
Despite initially struggling to place the ball on the spot to his satisfaction, for which he was booked, Costa made no mistake with his shot, placing the ball into the top-left corner.
David Luiz planted a header against the post from a Willian free-kick as Chelsea pressed for an equaliser, but Turan killed the tie in the 72nd minute by tucking home after his own header came back off the bar.
