The Reds got their 61st point to close the gap on United to four points, but the latter have a game in hand.
Cristiano Ronaldo put the hosts in front with a 23rd minute penalty, following Jose Reina's challenge on Park Ji-Sung.
Five minutes later, a rare blunder by Nemanja Vidic saw Fernando Torres robbing the Serb to slot home past Edwin Van der Sar in what proved to be a turning point in the game.
Three minutes before half-time, Steven Gerrard won a clever penalty from Patrice Evra, and the Liverpool skipper stepped up himself to fire home.
Vidic Nightmare
United carried on searching for a breakthrough and Sir Alex Ferguson made a hazardous move with a triple substitution 15 minutes from time.
However, the United tactician's attempts were shattered four minutes later when Vidic was given a straight red card after bringing down the unstoppable Gerrard, who was on his way to score.
Fabio Aurelio fantastically curled in the resulting freekick, leaving Van der Sar in total disarray.
Even though the three points were within their grasps at this stage, Rafa Benitez's men were not done yet.
Substitute Andrea Dossena, who came off the bench to score his first goal for Liverpool in the recent 4-0 drubbing of Real Madrid, put his name on the scoresheet again with an exquisite injury-time lob.