Torres' double put Barca ahead but they surrendered their two-goal lead as former Real Madrid playmaker Isco struck a brace of his own.
Joao Felix finished deftly in the 90th minute and Torres netted again to secure victory for the Catalans, who trail league leaders Madrid by seven points after Los Blancos scraped a 3-2 win over bottom side Almeria.
Girona, second, aim to reclaim top spot when they welcome Sevilla at Montilivi stadium later Sunday.
Torres, reaching a century of appearances for Barcelona since joining from Manchester City two years ago, was decisive and said he had worked hard for his moment.
"It's the fruit of hard work, discipline, consistency, of believing in yourself," Torres told Movistar.
"I'm going to enjoy it, and today is my 100th Barca game so I can't ask for more."
Barcelona handed young defender Pau Cubarsi his first start and along with Lamine Yamal, lined up with two 16-year-olds in the team.
The Catalans played well in the first half and controlled the game, a cut above their recent outings including the thrashing by Real Madrid last weekend in the Spanish Super Cup final.
Betis, ninth, did create one clear chance early on, with the magisterial Isco scooping a ball through for Luiz Henrique, but his lobbed effort beat Inaki Pena and the crossbar.
Torres put Barcelona ahead with a simple finish from Pedri's cut-back after Ilkay Gundogan's deflected pass found the midfielder in the area.
Robert Lewandowski, on a quiet afternoon for the former Bayern Munich striker, netted just before the break but it was disallowed for offside.
Torres doubled Barcelona's lead two minutes into the second half after the exciting Yamal drove to the byline and crossed for the Spain international.
However Isco soon pulled Betis level with a quick-fire brace.
The former Real Madrid playmaker rifled home after Pena only half-cleared a cross in the 56th minute and then timed his run well and cleverly hooked home Henrique's pass under three minutes later.
Late strikes
Xavi reacted by taking off Lewandowski for Brazilian starlet Vitor Roque, recently arrived from Athletico Paranaense.
Betis winger Henrique rampaged forward and nearly made Barcelona pay on the counter but flashed a shot narrowly wide.
The hosts were made to pay when substitute Felix produced a superb finish to give Barcelona the lead in the 90th minute and Torres made the game safe after Yamal sent him through.
Coach Xavi, under pressure in recent weeks, celebrated vigorously as Barcelona showed they will not relinquish their crown without a fight.
Isco was disappointed his team could not take anything from the game after fighting their way back from two goals down.
"We did the hard bit which was to pull level after going two down, when they had control of the game ... the team didn't give up, had faith, and at 2-2 we had chances to go in front," Isco told Movistar.
"We let them off the hook and in the end they have a lot of quality up front, and that made the difference."
