Man United took all three points, against the run of play, but down to the fact that LFC have almost no attacking quality in their current side.
Liverpool had made one change from the side that drew against Arsenal - midfielder Lucas Leiva replacing Jordon Ibe. Striker Benteke was named on the bench again.
The reds had the far better chances in the first half - taking advantage of Darmain being exposed at left back - with most of the reds chances coming down that side.
But LFC's lack of any quality finishing was evident in plentiful supply - good positions created - poor choices made and poor attempts on goal. On another day, maybe a couple of seasons ago, the likes of Sturridge and Suarez would have been walking off at half time with the match ball.
Fellaini was United's pick of the players in the first half - but he was given too much space by the reds at times and became embroiled in a running battle with Lucas Leiva mid way through the half.
Emre Can was trying to create chances but too often he was caught in possession or made poor passes - one backpass in particular almost causing trouble for the reds defence.
Sakho and Toure were equal to all of United's first half forays - shrugging off their recent injury concerns.
No changes for the second half - would Liverpool be made to pay for their first half errors.
Liverpool again started brightly - Emre Can powering forward and firing a shot that looked like it was going through de Gea's legs, but it took a deflection off the inside of his right leg that just did enough to take it wide.
Minutes later and it was Kolo Toure bursting into the opposition box before attempting a shot - it was blocked. Firmino fired way over the bar, Martial poked a shot wide, Mignolet didn't know how to deal with a backpass, Henderson fires a weak shot straight to de Gea.
It was low quality stuff from the two giants of English football.
The goal eventually did arrive and predictably it fell United's way. A cross in and Fellaini easily outjumped the reds defence to head it at the crossbar - the rebound smashed in by Wayne Rooney.
Liverpool reacted by bringing Benteke on but it was a little too late in the day to use a striker and United, a very poor United side, snatched all three points and completed another league double over Liverpool.
There is a growing feeling that this Liverpool side will need major surgery, and it doesn't look like the operation will start until the summer.