Salah got his side’s third to become the first player to score on the opening weekend in five consecutive Premier League campaigns and cap a fine display after earlier setting up Diogo Jota and Roberto Firmino.
The Reds were boosted before kick off by the return of talismanic defender Virgil van Dijk after 10 months out through injury and their day got even better when they took the lead midway through the first half.
Trent Alexander-Arnold found Salah inside the box and the Egypt forward’s touch fell into the path of Jota for the Portugal forward to finish clinically.
It was a little harsh on Norwich, who had made a spirited start to the game as they were roared on by a buoyant home crowd making the most of their return to Carrow Road and the top flight.
Teemu Pukki, who scored 11 goals in the Premier League two seasons ago, drew an early save out of Alisson after getting in behind the visitors’ defence.
But once Liverpool went in front they rarely looked in danger of letting their lead slip as Norwich struggled to rediscover their early rhythm.
Max Aarons cleared a goal-bound effort from Sadio Mane six minutes after the break but a second goal duly arrived shortly after the hour mark when substitute Firmino struck.
The Brazil forward had only been on the pitch for four minutes when he tapped in from close range after unselfish work from Salah, who opted to pass to his team-mate when he had the chance to shoot from a tighter angle.
Salah then wrapped up the perfect opening day for the Reds when he collected the ball after a corner had only been half cleared and curled a fine strike into the back of the net.