United were four goals down by halftime — 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.
“I think it is great to win 5-0 here, we knew before the game it would be tough if we did not play our game,” Salah said after the game.
“We knew they will come and try to give everything, so we had to give 100%.We just tried to play our football and play in between the lines to create more chances. We did that and were lucky to score.
“As long as the team keep winning I am happy and to give my best to the team to win.”
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.