United were four goals down by half time — the largest margin ever in their history at that stage of a game — and looked disjointed as Salah, Diogo Jota and Naby Keita all found the net.
Salah added his third moments into the second half before Paul Pogba was sent off for a dangerous tackle.
Bruno Fernandes had an opportunity to open the scoring for United after just four minutes but blasted over the crossbar.
Liverpool responded to the scare with a goal on five minutes after poor defending from United saw Luke Shaw attempting to mark Salah, Keita and Andy Robertson. Salah chose to play in Keita who hit the ball past David de Gea.
United were guilty of more poor defending on 13 minutes when Trent Alexander-Arnold put a low cross into the box and Jota stretched to place it in the net.
Salah scored his first goal on 38 minutes with a low sidefoot past De Gea and his second five minutes into added time at the end of the first half with a superb strike from the corner of the box.
The Egypt international completed his hat trick five minutes into the second half. His three goals on Sunday make him the top-scoring African player in Premier League history, overtaking former Chelsea forward Dider Drogba by two goals.
Cristiano Ronaldo thought he had pulled one back for United on 52 minutes with an excellent piece of individual skill but VAR replays showed he had been offside in the build-up and the goal was disallowed.
United’s day went from bad to worse when Pogba was sent off on the hour mark for a studs up challenge on Keita who had to be stretchered off the pitch.
