Atletico found themselves fighting an uphill battle right from the start on Saturday, as Valencia went three goals ahead inside 13 minutes and ultimately continued their unbeaten start to life under coach Nuno Espirito Santo.
It also condemned Diego Simeone's men to their first league defeat of the season.
Defender Miranda went into the match as Atletico's top scorer with three goals in La Liga, but he put the ball 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 keeper behind former Valencia hero Santiago Canizares' to save 13 Liga penalties.
Atletico ended the match with 10 men after substitute Alessio Cerci saw red for a second bookable offence in the 90th minute.
Valencia sit second with 17 points from seven matches, two shy of Barcelona.
Barca produced an immediate response to their European woes as they recorded a routine 2-0 win at Rayo Vallecano.
Luis Enrique's side suffered a 3-2 defeat at Paris Saint-Germain in Tuesday's UEFA Champions League clash, but Rayo offered no such threat as Claudio Bravo surpassed Pedro Artola's record of not conceding during the first 560 minutes of a Liga season.
Lionel Messi opened the scoring just after the half-hour, with Neymar following suit shortly afterwards.
Rayo improved again after the break, yet their chances of salvaging an unlikely draw slipped away following Jorge Morcillo's 60th-minute dismissal, while substitute Javier Aquino also saw red.
In other results, substitute Federico Piovaccari scored in the third minute of injury time as seventh-placed Eibar earned a dramatic 3-3 draw at home to Levante.
Malaga recorded an overdue 2-1 win over Granada, despite playing the final 18 minutes with 10 men, and Almeria came from behind twice to draw 2-2 with Elche.
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