The Blues were left reeling by a powerhouse performance from the Colombian star, which handed the European champions a dismal defeat in Monaco
The Colombian scored took his tally to six goals in two games as Los Rojiblancos won the trophy for the second time in three years, with Miranda adding a fourth in the second half before Gary Cahill hit a late consolation.
Chelsea named their strongest possible XI for the showpiece final, recalling Frank Lampard to the midfield in place of Raul Meireles as Fernando Torres started against his boyhood club.
On-loan keeper Thibault Courtois started for Atletico against his parent club, while Falcao led the attacking line on the back of his hat-trick in his side's last outing against Athletic Bilbao.
It was Falcao who looked the most dangerous from the off as Atletico came flying out of the blocks. The striker crashed an effort off the crossbar following a Felipe Luis cross just moments into the match and then David Luiz was fortunate not to give away a penalty as Chelsea’s defence struggled.
Atletico continued to open the match in furious fashion and, with just six minutes on the clock, that man Falcao broke the deadlock. The Colombian was played in behind the Blues back line and he cleverly dinked the ball left-footed over the onrushing Petr Cech, with Luiz unable to hook the ball off the line before it nestled into the net.
Chelsea tried to respond and Eden Hazard rifled a shot just over the bar, but just 10 minutes later, Falcao doubled Atleti’s advantage in sumptuous style, cutting inside Ashley Cole before curling a left-foot shot into the top corner past the despairing grasp of Cech.
The Blues were shell-shocked by the Europa League winners' start and tried to gain a degree of control on the ball, but their possession play lacked any real cutting edge and they were fortunate not to be down by three on the half-hour mark when Adrian Lopez somehow contrived to scuff Arda Turan’s cut-back off his own face before Falcao headed the rebound off the post.
The Spaniards continued to frustrate the European Champions as they pressed on the ball and denied the likes of Mata and Hazard any space to dictate play, and shortly before the break, Falcao completed a sensational hat-trick from another slick counter-attack.
The lively Turan held up the ball on the edge of the Chelsea box before sliding it through into the path of the Colombian, who took a touch to control before firing low through the legs of Cech to give the Spanish side a well-deserved three-goal advantage at the break.
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Chelsea began the second half with the same strong possession play but looked a shadow of the side which breezed past Newcastle in their last game. Atletico, meanwhile, looked consistently dangerous on the counter attack, particularly in wide areas. On the hour mark, they netted a fourth.
Chelsea failed to deal with a simple free-kcik into the box and the ball bounced off Falcao to Miranda, who poked beyond Cech at the near post as Cahill tried in vain to keep it from crossing the line.
Half-time substitute Oscar came close a few minutes later with a low drive from distance, but Atletico were playing with supreme confidence and the full backing of their vociferous support, and Cech had to react smartly to keep out a Koke free-kick which almost crept in at the far post.
Munich may have felt like a distant memory for Chelsea fans but they did have something to cheer when one of the heroes of that night, Cahill, rifled in low from close-range after Atletico failed to clear their lines from a corner.
Chelsea fans suddenly had something to celebrate but they were almost further embarrassed in the closing stages, as Cech saved smartly from Felipe Luis before Luiz turned a Turan cross towards his own goal but got fortunate as it rebounded against the post and bounced to safety.
The Blues pressed late on to try and restore a smattering of pride to proceedings, but in truth, the match - and the trophy - had been won at half-time by the blistering pace of Atletico's play and the brilliance of Falcao, who received a rapturous reception from all sides of Stade Louis II as he was replaced in the dying minutes.