Mali striker Frederic Kanoute had put Sevilla ahead from the penalty spot after 26 minutes, but former Spain striker Raul Tamudo engineered an outstanding equaliser in the second half.
Facing his own goal and with two defenders in attendance, Tamudo pulled the ball back and spun between his markers before beating the advancing Andres Palop with a cool near-post finish.
Striker Luis Garcia volleyed the winner with 10
Defending champions Barcelona, who drew 1-1 away at Levante on Saturday, stay top with 30 points, two ahead of Sevilla.
Third-placed Real Madrid, on 26 points, host struggling Athletic Bilbao in the Bernabeu later on Sunday.
Further down the table, Celta Vigo came back from two down to draw 2-2 away at Real Mallorca while Paco Flores got off to a poor start in his first game at the helm of bottom club Gimnastic, who lost 2-0 away at Villarreal.
Lille lose goalkeeper in fight-back win
Real beat Bilbao to close in on Barcelona