Gaizka Garitano's men were only promoted from Segunda Division last season, but Monday's crushing win sees them move into ninth - above Basque rivals Athletic Bilbao, who finished fourth last term.
Almeria had it all to do after just three minutes at Ipurua, as Federico Piovaccari seized on hesitant defending before finishing across goal.
Saul Berjon added Eibar's second in the 21st minute, beating Ruben via a deflection and their third arrived shortly after, Raul Albentosa heading past the unconvincing goalkeeper.
Soriano pulled one back just before the break, but the three-goal lead was restored again in the 57th minute, as Raul Navas exploited more questionable goalkeeping to head in Manu Del Moral's corner.
In the day's late kick-off, a 71st-minute equaliser from Rafael Martins rescued a point for Levante in a 1-1 draw at home to Getafe.
