The fightback enabled Chelsea to take advantage of Spurs' 2-2 draw with Everton at White Hart Lane where Gylfi Sigurdsson scored a late equaliser to rescue a point for the hosts in a pulsating game.
All three goals at Stamford Bridge were scruffy. Rafa Benitez's side went behind to a Cesar Azpilicueta own goal just before half-time but they were soon gifted an own goal of their own by Sunderland's Matthew Kilgallon following a lightning break by substitute Torres.
Defender Branislav Ivanovic then sealed victory for Chelsea in the 55th minute.
With 58 points from 31 matches, the European champions are ahead of Spurs on goal difference and also have a game in hand on their London rivals. Fifth-placed Arsenal are two points behind while Everton, in sixth, have 52.
Victory over Sunderland came in the same week Chelsea reached the FA Cup semi-finals by beating Manchester United 1-0 and edged closer to the Europa League last four by establishing a 3-1 lead over Rubin Kazan in their quarter-final first leg.
"Two days before the United game people said we were in a crisis, two hours before the game it was the end of the world and now we are in the top three again," interim manager Benitez told Sky Sports News.
With injury problems and because they are in the middle of a gruelling programme of five matches in 13 days, Chelsea have had to rotate their squad to keep the players as fresh as possible.
Demba Ba was forced off at half-time with an ankle injury after being on the receiving end of a heavy tackle and Torres came on to spark the Londoners into life against a Sunderland side playing their first game under new manager Paolo Di Canio.
The Spaniard, again wearing a mask to protect his broken nose, made an immediate impact by setting up Brazilian Oscar whose shot was deflected in off Kilgallon after Azpilicueta had messed up a goal-line clearance to give the visitors a surprise lead.
The Chelsea comeback was then completed by Ivanovic as he backheeled a mis-hit shot from fellow centre-half David Luiz into the net.
"In the first half we didn't start well," said Benitez. "We gave the ball away easily.
"But it was a very good reaction from the team in the second half, very positive. Fernando made an impact quickly, he was fresh and he was ready."
Earlier, Liverpool lost ground on the group chasing Champions League qualifying spots when they were held to a 0-0 home draw by West Ham United, leaving the Anfield club in seventh place with 49 points from 32 games.
West Ham are now six points clear of the drop zone in 12th position.
Newcastle United also pulled away from relegation trouble with a 1-0 win at home to Fulham thanks to Papiss Cisse's stoppage-time winner.
Victory lifted Newcastle to 13th with 36 points, a point behind West Ham.
Wigan Athletic remained in the
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