Former Liverpool striker Craig Bellamy returned to Anfield and put City ahead before Dutch forward Dirk Kuyt's late equalizer prevented the Reds from going down at home for the first time this season.
"When you are playing catch-up, you need to win, so we are disappointed," said Liverpool manager Rafael Benitez. "We lost two points but we still have to play at United so we will see."
Even though it had its shutout streak end at a British record 1,334 minutes, United chalked up its 10th straight league win with a 2-1 victory over Blackburn on Saturday.
Cristiano Ronaldo's free kick gave United the win after Wayne Rooney and Roque Santa Cruz exchanged first-half goals.
Dutch goalie Edwin van der Sar was rested in anticipation of Tuesday's UEFA Champions League game against Inter Milan, and Pole Tomas Kuszczak looked shaky in his place in the United goal.
Dutch manager Guus Hiddink's began his spell in charge of Chelsea with a 1-0 victory at Aston Villa that moved the Blues above Villa into third spot but still 10 points behind United. Nicolas Anelka scored the game's only goal.
"We had good possession, good triangles and were dangerous in the box," Hiddink, who replaced Luiz Felipe Scolari as interim Blues manager. "The only thing we didn't do was kill the game with the second goal and the second half we leaned back a little too much. But on the other hand we could have scored more."
Saturday also marked the EPL debut of Andrei Arshavin, a member of Hiddink's Russian national team. Arshavin went off in the second half after a disappointing outing for fifth-place Arsenal in a 0-0 tie with with Sunderland at home.