The hosts were the much better side in the opening exchanges at Ipurua and thought they'd taken the lead when Esteban Burgos tapped in from Sergi Enrich's flick-on.
The goal was initially ruled out for offside, but that decision was overturned and the goal stood after a VAR review.
Atletico had chances to get back into the game in the second half, with Santiago Arias seeing his volley bounce wide of the fair post just after the interval.
A few minutes later, the ball fell to Angel Correa on the edge of the area, but his shot was wide of the near post.
With 20 minutes to go, Alvaro Morata could only head into Marko Dmitrovic's arms from Saul's cross before Renan Lodi dragged his shot wide ten minutes later.
The win takes Eibar further away from the relegation zone while Atletico stay in third.