Sevilla, who have won only five of their 20 La Liga games this season, are 16th on 21 points, two above the relegation zone.
After missing captain Sergio Busquets to injury early in the match, the hosts were the better side for large parts of the game and controlled the pace.
Yet they could not make their dominance in front of goal count, with Sevilla keeper Yacine Bouno making two superb saves to deny Robert Lewandowski in the first half.
However, Barcelona looked sharp after the break, and opened the scoring when substitute Franck Casey showed great vision to put the ball on a plate for Alba Ghost in Sevilla’s defence, with the fullback slotting in in the 58th minute.
Twelve minutes later, Rafinha moved down the right and delivered a precise low cross to Gavi, who tapped it in.