Marcus Rashford two goals in the first half gave them a comfortable 2-1 victory over Liverpool at Old Trafford in the Premier League.
Manchester United were without Paul Pogba who was injured and was replaced by Rashford.
Roberto Firmino was looking for Mane at the back post as Liverpool tried to hit back, but his cross went a fraction too high.
Ashley Young played a dangerous looking ball towards Marcus Rashford as the home side stepped things up and then Nemanja Matic looked early for Romelu Lukaku, who was unable to make anything of it.
David de Gea’s goal-kick was flicked on to Rashford by Lukaku, and he brilliantly chopped inside of Alexander-Arnold and fired inside the far post.
With close to the half time, Mata could have made it three when Alexis Sanchez floated in a cross and his attempted kick flew narrowly wide.
Jose Mourinho made one change, by taking Rashford and replacing him with midfielder Marouane Fellaini.
Salah made an attempt to get Liverpool going in the opening moments of the second half, but Robertson was unable to reach his pass out wide.
Mane tried his luck from distance only to see the shot strike Eric Bailly and run straight to De Gea.
Mane tried another strike from the edge of the area but again United’s defence held firm, and at the other end Sanchez almost gave Alexander-Arnold the slip before Liverpool got the ball away.
Klopp side made another change by bringing in midfielder Georginio Wijnaldum for Alexander-Arnold, and Robertson for Dominic Solanke.
Salah in the sixth minute of stoppage time sliced a wild volley as United held on for a third successive league win.