The newly promoted side were bombarded with Liverpool attacks throughout the 90 as 27,000 fans watched on for the first time in over a year.
Salah finished the night off with a elegant to become the first player to score in five successive opening day fixtures in the Premier League.
Story of the game
Instinctive. Intricate. Inevitable. Mohamed Salah started off Liverpool's season like he had the previous five, with a goal. A beautifully whipped effort with his magical left boot marked him the first player to score on five successive opening days in the Premier League. New season, same Mo.
After a cross was headed clear from a Kostas Tsimikas in swinging corner, Salah was waiting patiently on the edge of the box to take control. He nudged the ball to his left and curled a shot towards goal. Tim Krul had no chance with the power on the shot firing past the goal keeper.
Krul had a busy day from the get go. In the opening minutes the Norwich shot stopper had to be quick off his line to deny Jota a chance at goal. The goal keeper was quick to rush out and head away the danger from Naby Keita's lifted ball.
The Netherlands international was called into action minutes later. Tsimikas' fancy footwork won the Reds a corner after he sold Todd Cantwell down the left flank and whipped in a dangerous cross towards Jota.
Liverpool's number 20 was hungry for his first goal of the season and had his header tipped over by Krul from the consequential corner.
Jota's hunger continued and he was rewarded in the 26th minute. Trent Alexander-Arnold's low driven cross cleverly found Salah on the edge of the box. Unintentional or not the Egyptian's loose touch fell perfectly into the path of Jota who had the calmness to poke home for his and Liverpool's first of the campaign.
The Portuguese had the least amount of touches on the field at the time but showed his instinct with a poachers goal.
Norwich replied in the form of their main man Teemu Pukki. Cantwell dinked a delicate ball over for Pukki who had a clear run on goal to level the scores. The Canaries striker had only the keeper to beat but shot to Alisson's near post giving the Liverpool 'keeper an easy save palming the shot away.
Jurgen Klopp's men were chomping at the bit the get the second half started. Jota set the standards by picking up the ball from his own half and starting a race of his own. He ignited the turbo and breezed past Norwich players with great close control before being wiped out just before the finish line by Cantwell. It was clear to see his specialist sprint training had paid off.
Norwich were pushed back in their own half and Liverpool came at them in relentless waves of attacks. The dam that was the City defence finally broke with Roberto Firmino dealing the final blow.
After coming on for the previous goal scorer Jota, Firmino was quick to replicate his counterpart. Mane's shot on the edge of the penalty area deflected perfectly to Salah. His brilliant vision and unselfish attitude assisted the goal as he drilled a fantastic ball across the box to Firmino who was left with an easy tap in once again and doubled the Red's lead.
Salah's expert finish then ended Norwich's return to the Premier League 15 minutes from time. But the Canaries gave it one last push resulting in a goal mouth scramble at Liverpool's end. Two brilliant point blank saves from Alisson kept the clean sheet in tact for Liverpool as Adam Idah came inches from scoring his first Premier League goal.