Saul Niguez opened the scoring early in the second period, before Antoine Griezmann doubled Atletico's lead 16 minutes from time as the capital outfit closed the gap on league leaders Real Madrid to nine points.
Neither side created a chance of note in the opening 20 minutes of action, although it was Eibar and their long balls into the Atletico box from wide positions that looked the most likely route to finding the game's first goal.
It took until the 26th minute for either side to have a shot on target, and that effort came from Eibar midfielder Adrian, whose low strike from an Ander Capa cross was saved by Miguel Moya in the Atletico goal.
Atletico had the chance to threaten from a 30-yard free kick in the 33rd minute when Fran Rico brought Koke to the deck, but Griezmann fired straight into the wall as a fairly tame contest remained goalless.
Indeed, the visitors failed to register a single shot on target in what was a disappointing opening 45 minutes, with Adrian's effort in the 26th minute proving the closest that either side came to making the breakthrough in the first period.
Eibar goalkeeper Yoel had to make a smart save to prevent Saul from scoring his second of the match just before the hour, before Pedro Leon missed the target down the other end as the score stayed 1-0 entering the final 20 minutes of action.
Atletico scored their second in the 74th minute when Griezmann converted a low Kevin Gameiro cross, however, and that proved to be the end of the scoring at the Ipurua as Simeone's side returned to the Champions League positions.