Diego Simeone's men 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.
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.
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.
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.
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.
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 nearly 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.
