Atletico captures the UEFA Super Cup
The Colombian scored all three goals in a mesmerizing first half, and hit the post twice. It was his second hat trick in five days, after scoring three times in a 4-0 victory over Athletic Bilbao on Monday.
Miranda completed the scoring for Atletico just after the hour mark. Chelsea dominated the possession but produced little of note, until defender Gary Cahill grabbed a consolation goal 15 minutes from time.
Falcao scored twice in last season's Europa League final to help Atletico to a 3-0 win against Athletic Bilbao, sealing its place in the European Supercup.
It's the second time Atletico has won the trophy.
The 26-year-old Falcao looked dangerous immediately, and almost gave Atletico the perfect start.
Filipe Luis made a superb run down the left flank and crossed in toward Falcao, whose diving header crashed off the crossbar, with Chelsea goalkeeper Petr Cech stranded.
Falcao did get off the mark in the sixth minute, though, collecting the ball from Gabi and drawing Cech towards him before firing the ball in off the far post. David Luiz tried in vain to clear off the line.
Chelsea almost restored parity immediately but Frank Lampard's fierce shot from about 25 yards was blocked by Juanfran.
It could have been worse for Chelsea as Mario Suarez found Adrian Lopez who streaked away from defender Branislav Ivanovic, but his shot was well blocked by Cech.
The Chelsea goalkeeper had no chance in the 19th minute when Koke picked out Falcao, who cut inside into the right side of the penalty area and curled an unstoppable left-footed shot into the top left corner.
Gabi could have extended Atletico's lead following a surging run, but Cech again did well to block.
Atletico seemed certain to score again 10 minutes from halftime. Arda Turan broke down the right flank and sent a ball across the face of the goal which eluded everyone before falling to Lopez, who scuffed his shot. Falcao then headed the loose ball against the post and Chelsea managed to scramble it clear.
Chelsea was dominating but the Spanish side looked dangerous on the counter. And it was from one of its speedy breaks that it scored again in first-half stoppage time.
Atletico cleared the ball following a Chelsea corner and Turan raced about 60 yards before slotting the ball to Falcao, who lashed it home for his 37th goal in 40 European matches.
Former Atletico idol Fernando Torres - who got a rousing cheer from the Spanish fans when his name was announced before the match - almost scored against his former club five minutes after the break, but he fired wide of the left upright.
More woeful Chelsea defending helped Miranda put the game out of sight on the hour mark.
Suarez knocked a free kick into Miranda's path, he chipped it over Cech and the ball crossed the line despite Cahill's efforts.
Chelsea scored in the 75th minute when Cahill fired in a low shot through a crowded penalty area following Lampard's corner.