Needing victory to reclaim the leadership from Real Madrid, the defending champions suffered their worst loss against Sevilla since a 4-0 defeat in 1951.
Robert Lewandowski missed a second-half penalty for Barcelona after Marcus Rashford had scored a left-footed volley in first-half stoppage time to give them hope of turning around a two-goal deficit.
Hansi Flick's side were second best for long periods and deservedly fell to their first league defeat of the campaign against a side who had not beaten them in the Spanish top flight for just over a decade.
Former Barcelona winger Alexis Sanchez opened the scoring from the penalty spot after visiting captain Ronald Araujo had bundled Isaac Romero over by the byeline.
Romero himself swept in the second goal from an incisive counter-attack before Rashford replied from Pedri's back-post cross.
However, a well-drilled home defence largely kept Barca at bay until Lewandowski put his spot-kick wide after former Manchester United winger Adnan Januzaj had fouled Alejandro Balde.
And when Jose Angel Carmona and Akor Adams scored in the closing minutes it compounded a miserable afternoon for Barcelona, who came into the contest after a midweek Champions League defeat by holders Paris St-Germain.
Barca remain two points adrift of Real Madrid, while Sevilla are fifth but could be overtaken by Atletico Madrid if they beat Celta Vigo in Sunday's late game. (BBC)
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