A fabulous strike from Jordan Henderson gave the Reds the lead, before a well-worked move saw Luis Suarez double their advantage before half-time.
Daniel Sturridge got his third goal in three matches for Liverpool soon into the second period, and that was followed by a great Steven Gerrard pile-driver and a Ryan Bennett own-goal.
Brendan Rodgers made four changes from the side that lost to Manchester United last time out as Pepe Reina, Martin Skrtel, Joe Allen and Raheem Sterling dropped out for Brad Jones, Jamie Carragher, Jordan Henderson and Daniel Sturridge.
Norwich boss Chris Hughton made four changes too, with the Canaries drawing 1-1 at home to Newcastle last week. Out went Sebastien Bassong, Anthony Pilkington, Wes Hoolahan and Simeon Jackson, and in came Ryan Bennett, Elliott Bennett, Jonny Howson and Grant Holt.
The match started with Liverpool controlling proceedings, knocking the ball around confidently in midfield without creating much, and Norwich nearly took the lead as Robert Snodgrass delivered an excellent free kick from the right, and Ryan Bennett’s header forced an easy stop from Jones.
Liverpool 5-0 Norwich
Liverpool continued to pass the ball well and their interchanging frontline was causing Norwich significant problems as Suarez played a pass through Bradley Johnson’s legs for Sturridge, but the England man’s resulting strike was halted by Mark Bunn in the Norwich goal.
Rodgers’ side eventually took the lead through Henderson, and what a goal it was as the England international struck a ferocious half-volley into the top corner of the Norwich goal after a Suarez effort was blocked.
It did not take the Reds long to double their lead as Lucas Leiva played a pass forward, only for Sturridge to take Michael Turner out of the equation with a clever dummy, allowing Suarez a free run on goal before sliding the ball past Bunn for his 20th goal of the season.
The second half followed an identical pattern in most respects as Liverpool continued to blow Norwich away with what looked like consummate ease and they soon had their third of the day.
Steven Gerrard picked out Stewart Downing in the right side of the area and the winger played the ball into the danger area first-time, with Daniel Sturridge on hand to tap it in from five-yards out.
Norwich’s introduction of Wes Hoolahan saw them attempt to offer some kind of riposte, but before long they were four goals down as the Reds’ captain came up with a trademark strike.
After Glen Johnson cut in from the left, he laid the ball off for Gerrard, and from between 25 and 30 yards out, he buried a shot into the bottom corner, giving Mark Bunn no chance.
Goal number five arrived with about 15 minutes to go, and it came in embarrassing circumstances as Sterling capitalised on some awful defending by Turner before crossing low towards Fabio Borini. However, Ryan Bennett got on the end of it and put it past his own goalkeeper.
The final stages saw Liverpool simply see out the match by knocking the ball around with ease, dazzling Norwich for the most part and ending without the visitors offering any kind of attacking threat.