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Espanyol came even closer just three minutes later, however, when Simao's free kick proved too good for the keeper but came back off the upright.
Sevilla's second goal came right on the stroke of half time as Vitolo's cross found Kevin Gameiro, who chested the ball down before slotting his shot into the bottom corner.
The visitors had a glorious chance to pull a goal back just two minutes after the restart, however, as Federico Fazio was penalised for a foul inside the penalty area.
Sergio Garcia stepped up to take the resulting spot kick and made no mistake with his effort, coolly finding the corner from 12 yards.
The hosts almost restored their two-goal lead in the 66th minute when Ivan Rakitic rose well inside the box, but he sent a powerful header just over the top.
Garcia had a chance to double his personal tally and draw his side level with 20 minutes remaining, but this time he couldn't find the target as he put his effort from inside the box narrowly wide.
The points were sealed for Sevilla six minutes from time when Marko Marin found Gameiro inside the box, and the French striker picked out the bottom corner for his second of the night.
There was still time for a fourth goal, however, as Rakitic capped off the scoring in the last minute of normal time to send Sevilla within three points of Bilbao.