The Red Devils snatched the derby win thanks to the goals of their Spanish attacking midfielder Juan Mata, while home team Liverpool's single goal was scored by English forward Daniel Sturridge.
Liverpool captain Steven Gerrard -- who came on as a half-time substitute -- was sent off in the 38th second after stepping on Manchester United midfielder Ander Herrera's foot. The Reds skipper Gerrard could stay on the pitch for 38 seconds.
In the 90th minute visitors Manchester United were awarded penalty kick after Liverpool player Emre Can brought down Daley Blind. Red Devils veteran forward Wayne Rooney missed the penalty from the spot.
Winning the game 2-1, Manchester United increased the point gap in standings to five against their closest opponents Liverpool.
Meanwhile, Brazilian football legend Pele was among the spectators at Anfield.