Vicente Iborra struck seven minutes from time to earn a 2-1 win that keeps Unai Emery's side on course to lift the trophy for the third straight year.
Timothee Kolodziejczak had levelled for Sevilla after Aritz Aduriz's opener.
There were also 2-1 wins for Shakhtar Donetsk and Villarreal against Braga and Sparta Prague respectively.
Yaroslav Rakitskiy put Ukrainian side Shakhtar in front in Portugal and Facundo Ferreyra pounced to make it 2-0 to the visitors before a late effort by home substitute Wilson Eduardo gave Braga hope.
Cedric Bakambu was the hero for Spanish side Villarreal with both their goals, either side of Jakub Brabec's equaliser for Sparta.
In Thursday's other quarter-final, favourites Borussia Dortmund were held to a 1-1 draw by Liverpool.
Holders Sevilla claimed their first away win of the season with a first-leg victory over Athletic Bilbao in the Europa League quarter-finals.