Atletico, who sold several top players in the close season including striker Diego Costa and defender Filipe Luis to Chelsea, took the lead when the unmarked Miranda nodded the ball in at the near post after 12 minutes.
Midway through the first half Croatian Mandzukic, bought from Bayern Munich in the close season, made it 2-0 when he headed a Gabi Fernandez free kick into the corner of the net from 12 metres.
Eibar, in their debut season in the top flight, refused to fold and responded in the 33rd minute with a fine curling shot by Abraham Minero from 20 metres that nestled in the top corner.
They pressed Atletico in the second half but the home side hung on for the victory.
Atletico, who have four points from two games this season, were presented with the league trophy ahead of the game.
"We started very well but were then unable to control the game," coach Diego Simeone told a news conference. "The anxiety to pick up the points affected us.
"We have to improve and work. Still it was a win which is positive and hopefully from here on our work will pay dividends.
"The characteristics of the players who have left are not the same as those who have come in. We are working hard so that the new players adapt," added Simeone.
"Obviously if you win then it means that you are more relaxed. It is a shame we now have a lot of players away for 15 days (on international duty)."
BILBAO TRIUMPH
Elsewhere, Aritz Aduriz, Ander Iturraspe and Iker Muniain were on target as Athletic Bilbao eased past Levante 3-0.
A second-half strike from Federico Cartabia gave Cordoba a 1-1 draw against Celta Vigo who had gone ahead through Fabian Orellana while Carlos Bacca and Vicente Iborra gave Sevilla a 2-1 win at Espanyol who replied through Christian Stuani.
On Sunday, Barcelona visit Villarreal and Real Madrid travel to Real Sociedad.
Eibar set out their stall to be solid and play on the counter-attack but soon found themselves behind.
Koke swung in a corner and Miranda was given plenty of space to head the ball home before the physical Mandzukic added a second goal.
Eibar were forced to change their tactics and the game opened up.
Antoine Griezmann shot wide for Atletico and at the other end Javi Lara forced keeper Miguel Angel Moya into a smart save from a free kick.
After a fine combination between Mikel Arruabarrena and Minero the latter struck a good effort beyond the reach of Moya to reduce the arrears for Eibar.
Just like Atletico's draw in their first match with Rayo Vallecano, the champions lacked intensity in the second half and Eibar wrestled away the initiative.
Angel Rodriguez had a golden chance to equalise but steered his effort wide three minutes from the end.
(Editing by Tony Jimenez)
Share
