Divock Origi, Mohamed Salah and Virgil van Dijk all got on the scoresheet on the opening day of the season.
Liverpool wasted no time in taking the lead, and it came through a dreadful error by Norwich captain Grant Hanley, who made a mess of Divock Origi's cross to divert the ball into his own net in the 7th minute.
Mohamed Salah kicked on from where he left of last season when he coolly fired into the bottom corner after Firmino fed him in the penalty area in the 19th minute.
Norwich's re-introduction into the Premier League took a turn for the worse after some slack marking allowed Virgil van Dijk to head in Salah's corner in the 28th minute.
Tim Krul in the Norwich goal, prevented Liverpool from adding a fourth just three minutes later, pushing away Firmino's volley in the penalty box.
It took until December last year for Divock Origi to make his first Premier League appearance of the season, but he took his chance from the start this season and crowned it with a neat header from Alexander-Arnold's cross in the 41st minute to register Liverpool's fourth goal of the night.
Norwich's attacking display was impressive throughout and they came close to scoring in the 63rd minute when Moritz Leitner struck the Liverpool crossbar with a fierce strike.
The travelling supporters finally had something to cheer about when Teemu Pukki tucked a shot beyond Adrian, on for the injured Alisson Becker, in the Liverpool goal for what proved to be a consolation goal.
