The Rojiblancos maintained their impressive form by overcoming the only side to have taken more points than them over the last six league matches, keeping them just about in title contention.
Eibar, who had won six and drawn one of their last seven matches either side of the winter break, remain two points outside the top six after their first defeat in over two months.
Atletico were looking very bright in the opening half-hour of the match and they had a lead to hold on to with 27 minutes played, as Antoine Griezmann was played clean through over the top and unselfishly squared for Gameiro to tap home.
Eibar offered a good response, with Charles heading narrowly over the bar as the home side went into the break having enjoyed more of the ball.
That continued to be the case as the match reached the hour mark, as Los Armeros threatened their opponents but failed to really create any serious clear-cut openings until 65 minutes in.
Atletico, whose only away league defeat since the start of 2017 came last time out at Espanyol, were having to dig deep as Eibar continued to build momentum.
Substitute Kike then flashed a header inches wide, but there was time for late drama as Fabian Orellana missed from point-blank range and Oliveira's header from the final chance was stopped by Oblak.
EIBAR (4-4-2): Dimitrovic; Ander Capa, Oliveira, Ramis, Jose Angel; Ivi (Orellana 46'), Jordan (Diop 73'), Dani Garcia, Inui; Charles (Kike 64'), Sergi Enrich
ATLETICO (4-4-2): Oblak; Vrsaljko, Gimenez, Godin, Hernandez; Correa (Carrasco 54'), Partey, Saul, Koke; Gameiro (Fernandez 69'), Griezmann (Torres 76')