The defending champions looked to be cruising when goals from Miranda and Mario Mandzukic, his first league strike 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.
Atletico had failed to fire in their season opener at Rayo Vallecano, but this match showed more promise when Antoine Griezmann powered over the bar after just 67 seconds.
And 10 minutes later the hosts were in front thanks to Miranda, who rose to meet a corner from Koke before heading in from close range.
A second goal followed in the 24th minute as Eibar's defence crumbled once more against a set-piece. This time it was a free-kick, which was whipped into the area by Gabi for Mandzukic to direct a header into the bottom left corner.
Eibar were in danger of conceding again minutes later when Griezmann fired narrowly wide of the right post from outside of the area.
However, the visitors showed signs of a fightback on the half hour, with Atletico goalkeeper Moya untidily clearing a free-kick from Javi Lara.
That should have served as a warning to Atletico, yet they allowed Eibar to pull a goal back after 34 minutes. Mikel Arruabarrena laid the ball at the feet of on-loan defender Abraham, who curled a delightful shot into the top right corner from 20 yards.
It was a wake-up call for the champions, who responded with an effort from Raul Garcia which was tipped over at full stretch by Xabier Irureta.
Diego Godin then planted a header wide as Atletico threatened again, but Eibar served a reminder of their presence four minutes before the interval with Mikel Arruabarrena's left-footed strike falling past the left post.
Neither side could gain the upper hand they so badly wanted as the minutes ticked by in the second half.
Raul Jimenez saw his 63rd-minute header matched by a save from Irureta, while Godin put another header from a Gabi free-kick wide of the left post.
It was a test of patience for Atletico coach Diego Simeone, who was watching from the stands as he serves an eight-match ban for his sending-off in the Spanish Supercup final.
And his frustration almost boiled over as he watched his players concede a 74th-minute free-kick, which was pumped into the area by Lara to an expectant Eneko Boveda, only for the Eibar defender to head wide from a few yards out.
The visitors then turned the pressure up another notch as the final whistle approached, and Angel thought he had done enough to secure a draw two minutes from time with his shot across the box on course for the bottom left corner.
However, Moya threw himself on the ground and claimed the decisive touch with a finger tip to divert the ball beyond the left post.