Luis Suarez scored a hat trick, and Liverpool scored five goals in all, as the Reds got their first win of the season.
Nuri Sahin - fresh from his double in the 2-1 League Cup win at West Bromwich Albion - and Steven Gerrard netted the other Liverpool goals in the second period with Steve Morison and substitute Grant Holt responding for the home side, who were probably lucky to get out of the afternoon losing by only three goals.
Suarez also scored a hat-trick in a 3-0 win for Liverpool at Norwich in April.
Incidentally, it was also the last time they enjoyed a clean sheet.
Norwich have now won just one of their past 11 Premier League matches, and have only three points from their opening six games of the season.