The Reds took the lead via Sadio Mane in first half hour as Fabinho's clipped ball inside was met by the winger, who controlled on his chest and slotted home.
United struck against the play as Romelu Lukaku's low cross was parried by Alisson, falling to Jesse Lingard who prodded home from close-range.
It didn't take long for the Swiss international to make his impact as he was found by Mane in the box before steadying himself and smashing the ball in to the roof of the net.
He sealed the victory minutes later as his deflected strike from outside the box sailed past David de Gea to give the Reds all three points on a cold wintery night at Anfield.
Liverpool are back to the top of the Premier League, a point above Man City and an astonishing 19 points ahead of Mourinho's United in sixth.
Slide through our gallery below for all the best snaps from a successful night at Anfield...