Mohamed Salah scored a hat-trick either side of half-time after Naby Keita and Diogo Jota had given Liverpool a 2-0 lead in the opening 13 minutes.
The win – which takes Liverpool second, a point behind Chelsea – was their biggest victory at Old Trafford.
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Jürgen Klopp’s side produced an astonishing display to defeat their fierce rivals in Sunday’s Premier League contest, with Naby Keita, Diogo Jota and Mohamed Salah (three) the goalscorers at Old Trafford.
Salah’s hat-trick took him to 15 goals in all competitions for Liverpool this season and the Egyptian has now scored in his last 10 games.
He flicked home Keita’s pull-back for his first goal, before curling a left-footed effort past David de Gea at his near post in first-half injury time.