Eibar joined Celta de Vigo as La Liga's surprise pace-setters after two games, as they downed Athletic Bilbao 2-0 on Sunday.
Saul Berjon's first-half penalty and Adrian's effort after the interval sent Jose Luis Mendilibar's men to the helm of the Spanish top flight, level on record with Celta - they have scored five goals and shipped one in their respective winning starts.
Supercopa de Espana holders Bilbao, meanwhile, prop up the standings - point-less through two games since ending their trophy drought against Barcelona.
Atletico Madrid are third in the table, preserving their flawless season with a 3-0 win at Sevilla.
Diego Simeone's men have not conceded in 180 minutes, and match Eibar and Celta's six points and plus-four goal difference - only to sit below them on goals scored.
Champions Barcelona are fourth (six points, plus-two).
Granada bounced back from their poor start to the season at home to Eibar, with a 2-1 win at Getafe.
Two goals in three minutes from Youssef El-Arabi and Isaac Success saw the visitors take the points from the Coliseum Alfonso Perez.
Valencia came from behind to draw 1-1 at home to Deportivo La Coruna, and the hosts finished with 10 men after Antonio Barragan was dismissed in the 84th minute.
Levante and Las Palmas both earned their first point of the season respectively, playing out a 0-0 draw.
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