Pablo Machin's side knew a win would take them top after Barca drew 1-1 with Atletico Madrid on Saturday and they seized an unconvincing success thanks to a close-range header from Portuguese forward Andre Silva on the half-hour mark.
Sevilla prevailed after the visitors' Turkish forward Enes Unal had two goals ruled out for offside in the second half.
It also took a flying save from home goalkeeper Tomas Vaclik to prevent substitute Unal equalising in stoppage time.
Sevilla now lead the standings on 26 points after 13 games, jumping ahead of Barca, who have 25.
Atletico are third on 24, with stuttering European champions Real Madrid sitting sixth on 20 after Saturday's humiliating 3-0 defeat at Eibar.
Sevilla coach Machin told reporters: "I wouldn't call it an epic victory, there were moments of uncertainty, but thanks to our defensive work and to Tomas, overall we deserved to win."
"You have to suffer to some degree in every victory and that's why we love football so much."
Espanyol missed the chance to move back into the top four as they were beaten 3-1 at home in a Catalan derby by Girona, whose former Espanyol striker Cristhian Stuani netted twice to move ahead of Lionel Messi as top scorer in La Liga with 10 goals.
Athletic Bilbao, meanwhile, are still searching for their first win since the opening day of the season after drawing 1-1 at home to Getafe, which means the Basque side, who have never been relegated, remain in the drop zone on 11 points.
