Wayne Rooney scored with Manchester United's only shot on target as Liverpool were stunned at Anfield.
The England International reacted quickest after Marouane Fellaini's header crashed off the crossbar to score his 176th goal in the Premier League for United and break Thierry Henry's goal tally for a single club.
A lacklustre first half, which included just one shot on target, saw Liverpool on top for the majority but guilty of poor finishing while Wayne Rooney saw little of the ball against Mamadou Sakho and Kolo Toure.
Marouane Fellaini and Lucas Leiva clashed twice early on, once when challenging for the ball before the United man pushed James Milner and the Brazilian took offence in the only flashpoint of the first half.
The second half followed in the same vein, with Liverpool and top, and Emre Can and Roberto Firmino were denied by a fine double save from David de Gea on the hour mark while United offered little elsewhere.
Both Juan Mata and Memphis Depay were thrown on to spark United into life and it worked, with the former supplying a cross to Fellaini who headed again the bar and Rooney smartly tucked in the rebound.
It was United's only shot on target during the game while Liverpool racked up nearly 20 attempts on goal.