The Colombian striker punished a defence missing the suspended John Terry and on three occasions struck with his left foot to put the game beyond doubt by the break after a sizzling series of counter-attacks by his side.
Brazilian defender Miranda headed in a fourth in a second half which featured a more assured Chelsea performance. Gary Cahill’s consolation strike with 15 minutes remaining was all that Roberto di Matteo’s side could muster.
Atletico’s success added to their Super Cup triumph of two years ago, the Spanish side beating Internazionale on that occasion.
Chelsea were on the ropes within minutes of the whistle; the incisiveness of Atletico midfielder Gabi’s passing matched by the clever movement of Adrian and Arda Turan.
All three were involved in Falcao’s opener, which came after seven minutes. As Arda and Adrian drew away Chelsea’s full-backs, Gabi threaded a neat through-ball into the area with Falcao clipping a left-footed shot over Petr Cech’s body and watching his effort glance off the post and into the back of the net.
The Colombian, who had already hit the bar before opening the scoring, was at it again 12 minutes later with his most impressive goal of the night as he beat Cech with a deft chip from the edge of the box, hitting the ball with his left toe as Cahill and the wayward David Luiz backed away.
Chelsea looked shell-shocked for much of the half, and could not muster a serious goal-bound effort despite the presence of Eden Hazard, Juan Mata and Fernando Torres and maintaining 58 per cent of the first-half possession.
Hazard succeeded only in winning a few free-kicks, but in his efforts to win one with a minute of the opening half remaining, he inadvertently let Atletico away with a break that led to Falcao’s third.
In a move indicative of Atletico’s sensational counter-attacking, Arda was left on the edge of Chelsea’s box with a multitude of passing options and nobody closing him down. He chose Falcao, who beat Branislav Ivanovic to the ball and poked in his third of the night and 42nd in just 53 games for Atletico.
Falcao, who received a standing ovation when he was replaced by Emre with four minutes remaining, was simply unplayable and added to his hat-trick of just five days earlier against Athletic Bilbao.
A combination of a dressing room dressing-down from di Matteo at half-time and Atletico’s willingness to sit on their advantage and break when necessary allowed Chelsea back into the game after the break.
The introduction of Oscar in place of Ramires was instrumental in their renaissance; the young Brazilian did not look at all over-awed by the occasion.
Afforded more time and space than before, the dynamic Hazard surged into the box on numerous occasions, although his efforts rarely did more than win his side corners.
His strike partner Torres – still revered by Atletico fans following a six-year stint at the Stadio Vicente Calderon earlier in his career – went close with a scuffed shot from the edge of the box that drew a save out of the Spanish side’s on-loan Chelsea goalkeeper Thibaut Courtois.
But it was defender Cahill who eventually did register a strike for the Champions League winners when the Englishman poked home a loose ball from inside the box after he and two Atletico defenders had failed to attack Frank Lampard’s corner.
By that time, however, Miranda had already added a fourth for Atletico; the Brazilian tapping in from close range after the excellent Mario Suarez had mis-hit his shot from eight yards out.
Di Matteo’s men, who have a 100 per cent record in the Premier League this season, would do well to wipe this one from memory. Their next opponents - Queens Park Rangers – certainly won’t pose quite such a stiff test of their resolve.