Diogo Jota opened the scoring in the 26th minute, having been selected to start alongside Mohamed Salah and Sadio Mane up front.
Roberto Firmino, recently back in training after Brazil's run to the Copa America final, replaced Jota with an hour played at Carrow Road and swiftly got on the scoresheet.
Salah claimed both assists – the second seemingly far more intentional than the first – and duly got in on the act, finishing emphatically with 16 minutes remaining and becoming the first player to score on five consecutive Premier League opening weekends.
Tim Krul extended himself to tip over an 11th-minute header from Portugal forward Jota before his opposite number was given some work.
Teemu Pukki got in behind the returning Virgil van Dijk on the end of Todd Cantwell's dinked throughball and Alisson had to save sharply at his near post in the 19th minute.
A pleasing back and forth had developed as Salah crashed a volley just wide from Mane's chipped delivery and it was Liverpool that found the breakthrough when the Egypt star failed to control Trent Alexander-Arnold's cross, with the ball falling kindly for Jota to slot home.
Salah made a truer contact on the volley when a left-wing corner was partially cleared, with his strike blocked by Ben Gibson before Pierre Lees-Melou got in the way of Joel Matip's follow-up.
Last-ditch Norwich defending continued early in the second half as Max Aarons and Grant Hanley combined to thwart Mane.
Konstantinos Tsimikas, playing at left-back for Liverpool in the absence of Andy Robertson, stung Krul's palms after the hour and the second goal inevitably arrived when Salah retrieved another blocked Mane effort and cut the ball into Firmino's path for a simple finish.
The goal Salah's endeavours deserved arrived when he snaffled a Gibson clearance and curled impeccably beyond Krul.