Eibar enjoyed a dream start to life in the Spanish top flight with a 1-0 success over Real Sociedad at the Estadio Municipal de Ipurua but, after losing 2-1 at champions Atletico Madrid, there were no further home comforts for the minnows on Monday.
Dominguez thrashed a powerful effort home from six yards after Eibar failed to deal with Juanfran's delivery from the right with just 13 minutes on the clock.
With a crowd of just 4,522 in attendance, Eibar struggled for inspiration and looked laboured against a Depor side happy to sit on their one-goal advantage.
And so Victor Fernandez sealed his first victory as Depor coach, lifting the visitors up to ninth, while Eibar sit 14th.
They are in good company, though, sharing the same points tally of three with European champions Real Madrid.
