Norwich captain Grant Hanley's hapless own goal just seven minutes in set the tone for what could be a long season for the Canaries before Mohamed Salah, Virgil van Dijk and Divock Origi made it 4-0 at half-time.
Teemu Pukki pulled a goal back for Norwich in the second half as Liverpool took their foot off the gas after the break.
The European champions are aiming to end a 30-year wait to win the Premier League after missing out by only one point to Manchester City last season despite amassing a club-record 97 points.
Much tougher tests lie ahead for Jurgen Klopp's men, but they picked up where they left off in winning their final nine Premier League games of last season and lifting a sixth European Cup in Madrid.