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Athletic Bilbao - Getty Images
Julen Lopetegui's side dominated the game but were dealt a late body blow when Athletic counter-attacked and striker Inaki Williams showed composure to lift the ball into the top corner.
The goal inflicted a first defeat on Sevilla since 6 March and snapped a five-game winning streak in LaLiga which put them among the contenders in the close-run title race.
The loss left Sevilla fourth in the standings on 70 points with four games to play, four behind second-placed Real Madrid and third-placed Barcelona and six from leaders Atletico Madrid.