The £12m summer signing scored from two deflected shots in the final quarter of the game to take his side above champions Manchester City at the summit.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Alisson; Clyne, Lovren, Van Dijk, Robertson; Fabinho, Wijnaldum, Keita; Mane, Firmino, Salah
SUBS: Mignolet, Moreno, Camacho, Henderson, Lallana, Shaqiri, Sturridge
STARTING XI: De Gea; Darmian, Smalling, Lindelof; Dalot, Lingard, Matic, Herrera, Young; Rashford, Lukaku
SUBS: Romero, Bailly, Valencia, Fellaini, Pogba, Mata, Martial
Jurgen Klopp: "We have to be angry on Sunday and we will be. We fight for our points. We have our own problems and targets. It's one of the games which you sign with your contract - try to do everything you have to win it. It's a big one, and if [former United boss] Sir Alex Ferguson says it's the British 'Clasico' then I am really blessed because I was involved in the German Clasico (Borussia Dortmund v Bayern Munich). It's a cool game."
Jose Mourinho: "We know that we are going to play against the leader, against a team on a high. But we have our qualities, we have our potential, even with the problems we have and the doubts in terms of team choice, of tactics, approach, philosophy. We have doubts about everything because we don't know who's available but we are going to arrive on Sunday and, with the players we have available, we are going to have a team capable of going there and fight for the victory."
LIVERPOOL SUBS: Mignolet, Moreno, Camacho, Henderson, Lallana, Shaqiri, Sturridge
MANCHESTER UNITED SUBS: Romero, Bailly, Valencia, Fellaini, Pogba, Mata, Martial