Thanks to a fast start against Brighton, Liverpool recorded their first triumph away from Anfield since February 15 on the South Coast.
Salah and Jordan Henderson were on target inside the opening eight minutes as the Premier League champions quickly seized control on the South Coast.
While a first away victory since a 1-0 success at Carrow Road on February 15 was made trickier by Leandro Trossard’s fine goal before break, Salah made sure of all three points when he headed in at a corner.
After going seven hours and 47 minutes without an away goal in all competitions, a barren run stretching back to Sadio Mane’s winner at Carrow Road, Liverpool scored twice within 127 seconds.
Naby Keita was influential in both goals, setting up the opener as he robbed possession from Davy Propper to tee up Salah, who curled in a first-time finish with his left foot.
Brighton failed to heed the early warning as they were pressed into trouble again soon after, Keita springing the counter from a turnover. Roberto Firmino and Salah were also involved before Henderson ran onto the ball to send a shot across Mat Ryan and into the net.
Alisson kept out Neal Maupay with a point-blank save but the Brazilian goalkeeper was left helpless by Trossard’s half-volleyed finish from a Tariq Lamptey cross, the sweetly timed strike halving the deficit.
Dan Burn then fluffed a glorious chance to equalise on the hour mark, scuffing his finish at the back post, and Salah made him pay.
The Egyptian forward took his tally to 19 in the league this season when his run to the near post allowed him to meet Andy Robertson’s set-piece delivery in the 76th minute, flicking the ball in as Liverpool moved 23 points clear of City.