Julen Lopetegui's team dominated the derby from the beginning and Ivan Rakitic opened the scoring in the 24th minute with a penalty after goalkeeper Claudio Bravo had tripped striker Youssef En Nesyri in a one-on-one challenge inside the area.
Four minutes before the break, Munir El Haddadi, who had come on minutes earlier for the injured Papu Gomez, took advantage of a mistake from the Betis defence to win the ball and put a low cross-shot between Bravo and his left post.
Sergio Canales scored the consolation goal for Betis in stoppage time with a perfect free kick from the edge of the box that went into the top left corner.
Sevilla moved up to 54 points from 26 games, eight ahead of Betis in third but still behind Real Madrid, who lead with 60.
After one win in their last five league games, Sevilla needed victory on Sunday to keep alive their ambitions of winning the title for the first time since 1946.
They stepped up with a convincing performance against in-form Betis, who had been honing in on second place as their local rivals struggled.
"We will fight until the end," Munir said.
"I started on the bench and was enjoying how my team mates were playing. Going on and scoring is awesome. Winning a Seville derby is incredible; it will be a long Sunday night of celebration for our fans."