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Basel opened the scoring on 34 minutes when Philipp Degen found Delgado, who rifled in a fierce effort from the edge of the box.
Delgado had his second of the evening four minutes later when he pounced to turn home Stocker's inviting delivery.
Los Che had two excellent chances to grab a goal back in quick succession in the second half, but neither Francisco Alcacer nor Eduardo Vargas could supply the finish after they had set each one another up.
Vargas then came even closer on 69 minutes when he headed just wide of the post after a good cross from Fede's cross.
Stocker then struck in stoppage time to give the home side a huge advantage ahead of the second leg at Mestalla.