Two first half goals from Marcus Rashford was the difference for Manchester United who gave away an own goal from the returning Eric Bailly in the second half.
It was again a tactical masterclass from Jose Mourinho who negated the Liverpool press by going back to front and that was how the two goals came.
On 14 minutes, a goal kick from David De Gea found Romelu Lukaku, who knocked it on for Marcus Rashford.
Rashford, recalled because of Anthony Martial’s injury, turned Trent Alexander-Arnold and fired an unstoppable shot past Loris Karius, in goal for Liverpool.
Ten minutes later, the same trick was repeated with Lukaku winning the header against Dejan Lovren. He teed up Alexis Sanchez, but a clearance fell to Rashford who found the net via a slight deflection from Alexander-Arnold’s heel.
Salah was in protective custody via the tenacity of Ashley Young and it was Bailly that provided the way back when he sliced his clearance beyond De Gea in the 66th minute.
Liverpool would say they had two valid penalty shouts which referee Craig Pawson waved away.
Salah had the last chance but he executed a poor volley with the chance to get the equaliser. United have now cemented their place in second place behind Manchester city with a five-point gap to Liverpool.