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The home side took the lead after just four minutes through Alberto Moreno, who drilled an effort into the bottom corner from a short corner.
However, their joy was short-lived as Markel Susaeta offered a reply two minutes later. It was a poor header from Federico Fazio that allowed Gaizka Toquero to gather the ball inside the area and tee up the midfielder from close range.
Gorka Iraizoz came to Bilbao's rescue when Fazio looked to atone for his error by meeting Votolo's corner with a bullet header after what had been a frantic opening half hour in Andalusia.
The game ebbed and flowed in the second half with both teams enjoys periods on top, although there was little in the way of clear-cut chances.
The result lifts Sevilla back above Getafe into seventh, while Bilbao remain in fourth place.