Fernando Torres opened the scoring five minutes past the hour mark when he raced onto a deft through pass from Yossi Benayoun and held off United defender Rio Ferdinand to fire into the roof of the net.
David Ngog made sure of the win in stoppage time after rounding off a quick breakaway move.
Both sides finished with ten men after the dismissal of United's Serbian defender Nemanja Vidic and Liverpool midfielder Javier Mascherano late in the game.
United fans threw numerous beach balls onto the pitch, in a mocking reference to Liverpool's defeat at Sunderland last week, but could not maintain their cheerful spirit until the end.
Liverpool, who suffered defeats to Sunderland and Chelsea in their precious two games and lost to Lyon in the Champions League, have 18 points from 10 games, four behind second-placed United and six adrift of leaders Chelsea.