Three goals in the first 13 minutes - including an own goal from Miranda - handed the high-flying hosts a stunning win as Alessio Cerci saw red late on
Diego Simeone's men found themselves fighting an uphill battle right from the start, as Valencia went three goals ahead inside 13 minutes and ultimately continued their unbeaten start to life under coach Nuno Espirito Santo.
Miranda went into the match as Atletico's top scorer with three goals in La Liga, but he put past his own goalkeeper to give Valencia the lead and their second arrived swiftly courtesy of Andre Gomes.
Although Nicolas Otamendi opened up a three-goal lead, Atletico should have been right back in the contest at half-time as Mario Mandzukic netted from close range, before Guilherme Siqueira saw his penalty saved.
In denying the spot-kick, Diego Alves became the second goalkeeper behind former Valencia hero Santiago Canizares' to save 13 Liga penalties.
Atletico enjoyed more of the possession in the second half as they desperately sought a draw, but their hopes were well and truly dashed in the final stages as Alessio Cerci received a second yellow card for handball and Valencia's unbeaten start to the campaign rumbled on.
Simeone backed Valencia as certainties for a top-four finish pre-match and the hosts showed why as they produced a fine display of relentless football in the opening stages.
It took Valencia just six minutes to break the deadlock as Miranda could only nod Antonio Barragan's deep delivery past his own goalkeeper as Miguel Angel Moya ran out to claim the ball.
Atletico were still reeling from the opener when the home side doubled their lead a minute later.
Andre Gomes, who has earned rave reviews since his close-season arrival from Benfica, skipped past a couple of challenges on the edge of the area, before confidently smashing low past Moya.
The champions' chances were crumbling before their eyes and they found themselves 3-0 down in the 13th minute.
Valencia goalkeeper Alves highlighted Atletico's set-piece prowess before the clash, but they failed to impress when defending them, as Otamendi capitalised on poor marking to nod in Pablo Piatti's corner.
Simeone's men appeared to have given themselves hope as Mandzukic headed in a rebound in the 29th minute, before Jose Gaya conceded a penalty for clumsily handling the ball.
But, Siqueira saw his spot-kick easily kept out by Alves, diving low to his right to comfortably hold the ball.
Atletico's control on proceedings continued to grow as the second half progressed.
But they struggled to create clear-cut chances, with their only opportunities coming from outside of the area.
With Atletico throwing men forward in an attempt to salvage something, Valencia almost notched a fourth on the counter, Rodrigo almost capping a week which saw him called up by Spain in by handing Sofiane Feghouli a goal, but the Algerian could not connect.
That mishap would go unpunished, though, as Cerci picked up a second yellow card for handball while attempting to score and Valencia held on for a deserved triumph, extending their unbeaten start in La Liga.