Salah's goal, which came in first-half stoppage time, gave Liverpool the lead and placed him in elite company, joining Ian Rush and Roger Hunt as the only players to reach 250 goals in all competitions for the club.
Ryan Gravenberch later sealed the win with a deflected long-range effort, moving Liverpool up to third in the Premier League.
The result ended Liverpool's four-game losing streak in the English top flight.
In another match, Amad Diallo scored a crucial goal for Manchester United in a 2-2 draw against Nottingham Forest.
Diallo's stunning 81st-minute volley rescued the draw for Manchester United, who had been leading at halftime.
The Red Devils had been down 2-1 before Diallo's goal, which was his first of the season.
Serhou Guirassy scored the only goal in Borussia Dortmund's 1-0 win over Augsburg, lifting them to third place in the Bundesliga.
Guirassy's goal, which came seven minutes before halftime, marked a vital return to form for the Guinean striker and moved him into second place in the Bundesliga scoring charts.
Guirassy's finish also served as a confidence boost ahead of Dortmund's crucial Champions League match against Manchester City.
Mohamed Amoura scored a brace in Wolfsburg's 3-2 loss to Hoffenheim, but his efforts were not enough to secure a win for his team.
Amoura's pace and movement troubled Hoffenheim's defense throughout the match.
Nicolas Jackson scored his first league goal for Bayern Munich since joining on loan from Chelsea in their 3-0 win over Bayer Leverkusen.
Jackson's goal doubled the hosts' lead just six minutes after Serge Gnabry opened the scoring on his 250th Bundesliga appearance.
Jackson also had another effort ruled out for offside and headed narrowly over as he led the line confidently in Harry Kane's absence.
Yan Diomande inspired RB Leipzig to a 2-0 victory over VfB Stuttgart, reclaiming their second place in the Bundesliga and ending the visitors' five-game winning streak.
Diomande created the opener just before halftime when his cross was deflected into the net by Jeff Chabot.
In the second half, Diomande showed his class again, weaving past two defenders before drilling a precise left-footed strike beyond Alexander Nubel.
Abde Ezzalzouli scored a goal for Real Betis in their 3-0 win over Mallorca, capping a commanding performance from the Moroccan winger.
Ezzalzouli's goal came in the first half, and he sealed the win after Antony had already scored two goals for Betis.
Betis dominated the match, climbing to fifth in La Liga and edging closer to the Champions League places.
Habib Diallo inspired Metz to a vital 2-0 win over Nantes, earning their second straight Ligue 1 victory and lifting them off the bottom of the table.
Diallo's late goal capped a disciplined Metz display that extended their unbeaten run and deepened Nantes' struggles at home.
Moses Simon scored the decisive goal in Paris FC's 1-0 win over AS Monaco, ending the hosts' six-match unbeaten run.
Simon's goal came after a tense first half, and he sealed the result on a counter-attack, racing clear to fire past Anthony Lopes with precision.











