The Egyptian national team captain scored twice as the Reds defeated Bournemouth 2-0 at the Vitality Stadium on Saturday.
Salah broke the deadlock on the half-mark before sealing the win with a 75th minute penalty.
The result left the Merseyside club on top of the league standings with 56 points from 23 games - nine clear ahead of Arsenal ahead of their clash with fourth-placed Manchester City on Sunday.
Salah is the league's current top-scorer with 21 goals for the season. His two recent efforts saw him move onto 178 overall Premier League goals, and surpass former Chelsea midfielder Frank Lampard into sixth place on the list of players with 100 or more Premier League goals.
Speaking after his brace, a delighted Salah said on Sky Sports: "It feels good to be fair! Scoring goals, team winning, it's an incredible feeling.
"But I said many times before that my main target this season is to win the Premier League with the team.
“We are going in the right direction so hopefully we can keep going like this.”
Tyrell Malacia admits he cannot wait to be "finally playing good football again" after finalising a move to PSV Eindhoven as one of two beat-the-deadline deals confirmed by Manchester United.
Liverpool manager Arne Slot has confirmed that Trent Alexander-Arnold will miss the second leg of the Carabao Cup semi-final against Tottenham on Thursday.
Mikel Arteta has relayed his frustrations at Arsenal not being able to recruit an attacking addition during the January transfer window.
Alphonso Davies has quashed any hopes Real Madrid had of signing him as a free agent this summer by committing his future to Bayern Munich.
