The defending champions looked to be cruising when goals from Miranda and Mario Mandzukic, who scored his first league goal since joining from Bayern Munich over the summer, gave them a cushion on home soil.
But Abraham pulled one back for newly-promoted Eibar and they could have snatched a point in the dying minutes but for a timely intervention from goalkeeper Miguel Moya to deny Angel Rodriguez.
Athletic Bilbao got their first win of the season at the second time of asking as they comprehensively beat Levante 3-0 earlier on Saturday evening.
Having lost narrowly at Malaga a week ago, Ernesto Valverde's men got their season up and running in some style at San Mames.
Aritz Aduriz got the opener 32 minutes in and Ander Iturraspe erased the prospect of any late nerves with a second after the break.
It was party time after that and Iker Muniain added a third 13 minutes from the end.
Primera Division new boys Cordoba enjoyed a happy homecoming back in the top flight, coming from behind to salvage a 1-1 draw at home to Celta Vigo.
Fabian Orellana gave Eduardo Berrizo's side the lead early in the second half with a fortuitous goal that owed a lot to a lapse in concentration by Cordoba goalkeeper Juan Carlos, but Fede Cartabia saved his team-mate's blushes by thumping in an equaliser seven minutes later.
That gave the Andalusian side their first point of the season following last week's 2-0 defeat at Real Madrid.
Sevilla won 2-1 at Espanyol in the late game to take their tally to four points from two games.
Carlos Bacca put them ahead in the 34th minute and Vicente Iborra's header made it 2-0 in the 57th minute.
Christian Stuani pulled a goal back for Espanyol with a header four minutes later but the home side were unable to find an equaliser.