Chelsea could have little to complaint about following the loss at Anfield, though Blues manager Luiz Felipe Scolari insisted the red card to midfielder Frank Lampard for a tackle on Liverpool midfielder Xabi Alonso was unjust.
Torres, who had not scored a league goal for the Reds since October, was invisible until he broke the game open with goals in the 89th minute on a header off Fabio Aurelio's cross and in stoppage time after Israeli Yossi Benayoun stole the ball from Ashley Cole.
United's win on Cristiano Ronaldo's penalty kick was its seventh straight Premier League triumph.
Goalie Edwin van der Sar extended his shutout streak to 1,122 minutes, beating the previous English league record of 1,103 set by Reading's Steve Death in the 1978-79 season.
"It's a fantastic performance," United manager Alex Ferguson said. "I couldn't believe it when I read that the last [EPL] goal we conceded was against Arsenal in November."
Fourth-place Aston Villa and fifth-place Arsenal had to settle for 0-0 ties with Wigan and West Ham, respectively. Villa is now tied with Chelsea, while Arsenal trails Manchester United by 10 points.