Diego Simeone's side needed to win in Catalunya to climb back above Valencia but their cause was completely undone by the first-half dismissal of Miranda
The champions, looking to bounce back from consecutive league draws with Sevilla and Valencia, produced a toothless performance at Cornella-El Prat that leaves them fourth in La Liga.
Although Diego Simeone's men created the better chances before the break, their struggles were evident throughout.
The physical Felipe Caicedo proved a nuisance and the hosts' resolute backline kept Fernando Torres quiet until his withdrawal following Miranda's sending-off.
Torres and Antoine Griezmann did both spurn good chances, while Raul Garcia saw a couple of late efforts denied.
But Sergio's side were more prominent after the break and only a fine defensive performance kept them at bay.
Despite Tuesday's crucial Champions League last-16 second leg against Bayer Leverkusen on the horizon, Simeone refused to rest key men for Saturday's trip.
The hosts looked capable of causing problems for Atletico during the early exchanges, with Caicedo and Sergio Garcia particularly lively.
But Atletico's set-piece prowess soon caused panic in the Espanyol defence, as Torres headed on Koke’s 11th-minute free-kick delivery to force Kiko Casilla into an acrobatic save.
Koke then went close himself from the resulting corner, lashing a half-volley agonisingly wide of the bottom-left corner.
Espanyol's willingness to throw men forward left them exposed in the 22nd minute, though they escaped unpunished when Griezmann dragged an effort off target at the end of a swift Atletico breakaway.
That scare saw the home side begin to take fewer risks, but they received a significant boost to their chances just before the interval, as Miranda was shown a straight red card for clattering into Abraham with a raised elbow.
Torres was replaced by centre-back Jose Maria Gimenez as a result of Miranda's indiscretion and with that change, Atletico's attacking threat effectively vanished.
The numerical advantage allowed Espanyol to exert more control, though Diego Godin and Gimenez proved an able shield to keep them at arm's length.
Atletico sat back for a great deal of the second half, but they finally crafted another chance with 13 minutes to go when Raul Garcia saw Casilla parry his effort away after he had latched on to Griezmann's clever flick.
The midfielder was denied by Casilla again a few moments later, the goalkeeper blocking a shot from point-blank range, as both sides failed to find a late breakthrough.