Brendan Rodgers' side claimed its first three points of the season with the Uruguayan striker once again running riot at Carrow Road leaving Chris Hughton without a win
In addition to Suarez's three goals, Real Madrid loanee Nuri Sahin and team captain Steven Gerrard added a goal a piece. Steve Morrison and Grant Holt scored for the Canaries.
Luis Suarez opened the scoring inside two minutes before adding another just before the break to give Brendan Rodgers' side a comfortable lead at half-time.
The Uruguayan then completed his hat-trick after the break before Nuri Sahin netted his first league goal for the Reds. Steve Morison and Grant Holt then managed two consolation efforts for the Canaries either side of Steven Gerrard's deflected strike.
Wes Hoolahan made way for Simeon Jackson in Hughton's one change from Norwich's last league outing.
While Rodgers made three changes from the side which lost to Manchester United last week. Sahin and Suso were recalled to the lineup after impressive midweek performances in the league cup and Andre Wisdom made his Premier League debut in defense.
Norwich should have pulled one back straight from the second half kickoff, when Andrew Surman's shot across goal was some how scooped over the bar by Robert Snodgrass a yard out from goal.
Norwich was made to pay for the wastefulness immediately as Suarez turned provider and squared a ball across the box for Sahin to simply stroke it into the goal in the 48th minute.
And ten minutes later Suarez completed his hat trick. Sahin found the Uruguayan cutting in from the left and the striker got his third with a curled effort round Ruddy, with the help of a small deflection.
Morison did manage to pull one back for the hosts on the hour. The Wales striker latched on to a loose ball in the box after Reina made a couple of quick saves but he parried towards the striker, who fired home on the half volley.
Only for Liverpool to restore its four goal lead via its captain Gerrard eight minutes later. He stroked home Sterling's low cross with his shot taking a heavy deflection, completely wrong footing Ruddy on it's way into the net.
Suarez could have even made it six in the 72nd minute with his jabbed effort from close range only trickling a yard or so past the post.
Liverpool dominated possession for the remainder of the match and were coasting to the final whistle when Holt capitalized on Skrtel's miscue to bend a fine low shot past Reina to add another for the hosts.
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