Messi's first came from a superb volley before he curled home from the edge of the area and then clipped in a neat finish to complete his treble.
It was the 32nd hat trick of Messi's La Liga career, while he has notched eight in the Champions League, three in the Copa del Rey, one in the Spanish Super Cup and six in international competition with Argentina.
He is second in the all-time La Liga list behind former Real Madrid star Cristiano Ronaldo, who has 34, but the two are tied on 44 club hat tricks in all competitions.
That makes them the joint holders of the all-time record for the most hat tricks scored for a club in Spain.
Messi leads the statistics for Europe's five major leagues, with 25 goals and 11 assists so far this season.
His treble moved Barca 10 points clear at the top of La Liga ahead of Atletico Madrid's game against Villarreal on Sunday, but speaking after the match, he said they were not getting carried away.
"No, that's not one hand on the title -- there is still a long way to go," he told beIN SPORTS.
"But it was an important win because it helps us maintain our lead over our rivals. It's always tough to win [at Sevilla]. They always make it difficult.
"You go through different spells in a season. You can't always play at a great level. We have been on a run -- if we're being honest -- in which we have not been playing our best football. But today we were back to being ourselves."
Barca's win came after a run of one victory in five games and sets them up for this week's double-header against rivals Real Madrid.
They face Madrid at the Bernabeu twice, first in the Copa del Rey semifinal first leg on Wednesday and then in the league on Saturday.
"All [competitions] are important for us," Messi said. "We don't throw any competition. We are one step from a final in the cup. It is going to be a really tough game because it's against Real Madrid and it's at their ground, but we're going there to win and we're confident we can do it.
"After that, we will think about the La Liga game there -- but we want to win everything."
Information from ESPN FC's Sam Marsden was used in this report.