The Catalans had not won at home since beating Rayo Vallecano in October but they produced a gutsy display and nearly took the lead in the first half when defender Bernardo Espinosa headed against the crossbar.
Sevilla's Argentine midfielder Ever Banega was sent off deep in stoppage time for kicking out at Girona captain Pere Pons, compounding the visitors' frustration at missing out on a chance to gain on their rivals for fourth place in the standings.
Joaquin Caparros's side are fifth in the table after the defeat but locked on 55 points with Getafe, who can go three points clear if they win at Real Sociedad later on Sunday.
Valencia, who were beaten 1-0 at home by Eibar earlier on Sunday, are sixth on 52 points.
Girona meanwhile boosted their chances of staying in the top flight by leapfrogging Real Valladolid, moving two points above the drop zone with three games remaining.
(Reporting by Richard Martin; Editing by Toby Davis)
