The Brazilian's header settled a tight affair at the Estadio de los Juegos Mediterraneos.
Miranda scored his second goal in as many games as Atletico Madrid ended its wait for a win at Almeria with a 1-0 La Liga victory.
The Brazilian defender was on target in a disappointing 2-2 draw with Celta Vigo on Saturday, and took his tally to three goals for the season with a second-half header to secure all three points in Andalusia on Wednesday.
Atletico had never won in five previous visits to Estadio de los Juegos Mediterraneos, including a 2-0 defeat last term, but did enough to secure victory despite not being at its best.
The defending champions were lacking a spearhead in attack in the absence of Mario Mandzukic, who is recovering from a broken nose, but coach Diego Simeone got the clean sheet he asked for as he watched from the stands while still serving a touchline ban.
Goalkeeper Ruben pulled off some fine saves for the home side, which was brought back down to earth following a 2-1 win at Real Sociedad at the weekend, but was unable to prevent Simeone's men securing their third league win of the season.
Atletico captain Gabi dropped to the bench along with Cristian Ansaldi and Raul Jimenez as Guilherme Siqueira, Raul Garcia and Mario Suarez came into the starting lineup.
Mane replaced the suspended Sebastian Dubarbier in the Almeria side, while Fran Velez and Wellington Silva also started in place of Edgar Mendez and Thomas Partey, who was ineligible to face his parent club.
Atletico was not allowed to settle in a frantic first half, but Antoine Griezmann ought to have done better with a tame header after Mario Suarez picked him out just seven minutes in.
Simeone's side started to get into its stride and Tiago let fly with a long-range strike that forced a fine reflex save from Ruben just before the half-hour mark. Ruben then came to Almeria's rescue once again five minutes before the break, palming away a left-footed strike from Raul Garcia following a slick Atleti move.
Saul Niguez replaced Suarez at halftime and Simeone's side continued to look the more likely to open the scoring early in the second half. Griezmann beat the offside trap, but the France forward was indecisive as Ruben raced off his line to narrow the angle and the chance passed.
Atleti had looked dangerous from set pieces throughout and it came as no surprise when it was an inviting corner from Koke that provided the opening goal. The Spain international swung the ball over with pace from the right and Miranda rose highest to head home at the near post on the hour mark.
The impressive Ruben produced another excellent save to deny Arda Turan a second goal 68 minutes in after the Turkey winger had cut in from the left at pace.
Verza fired a late free kick narrowly wide as Almeria applied some late pressure, but the visitors stood firm.