Saido Mane scored his 100th goal for Liverpool in a 3-0 win against Crystal Palace.
The Senegalese star opened the scoring for the hosts just before halftime.
Salah added the second goal before Naby Keita completed the rout with the third goal to send Liverpool top.
Mane has scored in nine consecutive games against Crystal Palace.
Liverpool have now won four out of their five opening Premier League games.
Manchester City played out a disappointing 0-0 draw against Southampton at the Etihad Stadium.