Captain Steven Gerrard gave Liverpool the lead for good just before halftime after Fernando Torres tied the score following Cristiano Ronaldo's penalty kick for United.
"It was magnificent, a great team performance," Gerrard said.
The Reds' first win at United in five years — and manager Rafa Benitez's first — was put beyond doubt in the last 15 minutes, with goals by Fabio Aurelio and Andrea Dossena as the defending champions were humiliated by their fiercest rival.
This was United's worst home defeat since a loss by the same score in 1992 against Queens Park Rangers. The club's miserable afternoon was compounded when defender Nemanja Vidic was ejected for the second time this season against Liverpool.
United is still four points ahead of Liverpool with a game in hand.