Steven Gerrard scored twice from the penalty spot and Luis Suarez netted his 25th goal of the season to complete a win which underlined the huge gulf in quality between the two sides.
Gerrard converted from 12 yards after Rafael handled the ball and the Liverpool captain scored again from the spot when Phil Jones knocked over Joe Allen after the restart.
The England skipper would have scored Liverpool's first hat-trick at Old Trafford since 1936 if his third penalty had not hit a post after a foul was awarded against Nemanja Vidic for a challenge on Daniel Sturridge.
Vidic was sent off for the tackle - the fourth time he has been dismissed against Liverpool - but replays appeared to show Sturridge had dived to win the spot-kick.
Suarez then rounded off the rout near the end with a well-taken finish.
The scoreline did not flatter Liverpool at all. They thoroughly deserved it.
Shouts of 'ole' rang out as the Reds played keep ball while United tried to chase it down.