The win sees Xavi Hernandez's team climb to fourth place in the standings with 45 points, 15 behind leaders Real Madrid and ahead of fifth-placed Atletico Madrid on goal difference in the hunt for Champions League qualification.
Xavi has steered his squad to recent results, including a midweek win over Napoli that saw them advance to the last-16 in the Europa League. When asked about his side's hopes of challenging for the LaLiga title, the manager said they are taking it all in stride.
"I've said that we're not ruling anything out. Madrid are strong, as are Sevilla. We have to climb the table. We're working with all the humility in the world, taking things game by game. Now we prepare for Elche next week," Xavi said. "Nothing else. We have to remain humble and keep working hard."
The second goal came in the 73rd with a fantastic finish by substitute Ousmane Dembele, who made peace with the Barca fans and received a standing ovation after almost leaving the club in January due to his reluctance to renew his contract.
The French winger received a long pass from Luuk de Jong just outside the box, cleared a defender and fired a bullet of a shot that flew past the goalkeeper into the top left corner of the net.
Dembele provided assists for the third and fourth goals, in stoppage time. First, he crossed perfectly to De Jong, who scored with a header, then, in the final play of the game, to Memphis Depay, who stroked in a volley from close range.
Xavi praised Dembele's efforts in the match, amid tension between the player and the fans.
"There weren't many whistles for Ousmane. The fans rule and they can do what they want, but they have to be on our side," Xavi said. "Ousmane's a great professional who supports the group and is a good guy in the dressing room. He can make the difference on the pitch. That's the best Dembele we have seen today. The fans should support him, he's a professional."
Xavi was also complimentary of Pedri's command in the midfield, saying "I have not seen a player with that talent in the world.
"There isn't that talent [anywhere else]. It doesn't exist, honestly. He doesn't like to be praised, but I'm saying it clearly how it is, knowing how humble he is."
ESPN correspondent Sam Marsden contributed to this report.