The away side entered the match as the firm favourites following a 3-1 win when the two sides met in the first leg at the San Sebastian last week.
The game had been in doubt due to Racing threatening to strike over unpaid wages and that indeed proved to be the case as the referee was forced to suspend proceedings after the home side refused to play.
Sociedad will now face Barcelona in the semi-finals.
RACING: Mario; Francis, Garcia, Orfila, Barrio; Andreu, Ayina, Soria, Granero; Miguelez, Duran
SOCIEDAD: Zubikarai; Zaldua, Mikel, Inigo, Angel; Gaztanaga, Ros, Zurutuza, Prieto; Seferovic, Castro