The striker netted in the 15th, 29th and 35th minutes to become the first Premier League player to score three hat-tricks against the same team.
But the 26-year-old refused to rest on his laurels and netted a fantastic free-kick on 74 minutes before Bradley Johnson headed home a consolation for the Canaries with seven minutes remaining.
Suarez then turned provider for Raheem Sterling to score late on to round off the win, which was just the tonic for Brendan Rodgers' side after their disappointing defeat to Hull City last time.
Suarez now has 11 goals in five appearances against Norwich and he did not score in his first game against them. In his last four appearances he is averaging a goal every 33 minutes.
Ian Rush was the club's all-time top scorer against Norwich with nine and it took him 21 matches. Suarez effortlessly breezed past him, having begun the day level with David Fairclough and the watching Kenny Dalglish.
The bigger picture shows Suarez's 50th league goal for the Reds came up in only his 85th game and in doing so took the outright lead as the Premier League's top scorer this season with 13 in nine matches.
After 15 minutes of frustration born out of mis-placed passes normal service was resumed at Anfield, where Liverpool have now scored 13 on their last three appearances.
John Ruddy's kick was headed forward by Steven Gerrard and, when Leroy Fer missed his clearance, that was the cue for Suarez to seize his chance, half-turning towards the Kop to lash a dipping inch-perfect shot over and across the Norwich goalkeeper from 35 yards.
It was reminiscent of the goal he scored at Carrow Road in April 2012 when he netted the first of his three hat-tricks against them.
His second, just before the half hour, was a more instinctive finish but no less clinical.
Philippe Coutinho swung over a left-wing corner and Gerrard ducked underneath the ball to give Suarez the opening he needed and quick as a flash he hooked home left-footed.
His hat-trick came six minutes later when the helpless Fer could only look on as Suarez flicked the ball over his head a la Paul Gascoigne versus Scotland at Euro 96 before skipping past the midfielder to lash past Ruddy.
Norwich resorted to fouls with Johnson booked for a trip just as Suarez looked set to break through the heart of the defence but the damage had already been done.
Strangely Norwich, buoyed by their weekend win over Crystal Palace, had created the first two scoring chances with Jonny Howson firing over and Wes Hoolahan's low strike saved by Simon Mignolet.
Suarez ended any fanciful hopes they had of recording a first Anfield victory since April 1994.
Conjecture at the interval was whether Suarez could maintain his form and score a hat-trick in each half.
He showed he is merely magical and not miraculous with just one more goal in the 74th minute, although that too was a thing of beauty in its own right.
Gerrard was brought down by Howson 25 yards out and, after Coutinho had failed with their previous effort from a similar position, Suarez stepped up to curl a shot up and over the wall and into the net.
Johnson headed home Nathan Redmond's left-wing cross with seven minutes to go before Gerrard hit the post with a cheeky volley.
Sterling then ensured the night finished on a high by converting Suarez's cross on 88 minutes.
This was the sort of performance Liverpool needed to put on at the weekend at Hull, the start of three matches in a week which they were expected to win.
Defeat there was a missed opportunity to consolidate second place and they dropped to fourth - which is where they remain as their UEFA Champions League-chasing rivals also won.