He also formed a threatening new partnership with £12million signing Daniel Sturridge.
Rampant: Liverpool ran riot at Anfield as Norwich were put to the sword in a clinical display
MATCH FACTS
Liverpool: Jones, Wisdom, Carragher, Agger, Johnson, Gerrard, Lucas (Sterling 68), Henderson (Allen 77), Suarez, Sturridge (Borini 69), Downing.
Subs Not Used: Gulacsi, Shelvey, Skrtel, Robinson.
Booked: Johnson.
Goals: Henderson 26, Suarez 36, Sturridge 59, Gerrard 66, Ryan Bennett 74 og.
Norwich: Bunn, Martin, Ryan Bennett, Turner, Garrido, Elliott Bennett (Hoolahan 65), Johnson,Howson, Snodgrass (Pilkington 86), Tettey, Holt.
Subs Not Used: Rudd, Jackson, Barnett, Tierney, Kane.
Booked: Snodgrass.
Att: 44,901
Ref: Michael Oliver (Northumberland).
Subs Not Used: Gulacsi, Shelvey, Skrtel, Robinson.
Booked: Johnson.
Goals: Henderson 26, Suarez 36, Sturridge 59, Gerrard 66, Ryan Bennett 74 og.
Norwich: Bunn, Martin, Ryan Bennett, Turner, Garrido, Elliott Bennett (Hoolahan 65), Johnson,Howson, Snodgrass (Pilkington 86), Tettey, Holt.
Subs Not Used: Rudd, Jackson, Barnett, Tierney, Kane.
Booked: Snodgrass.
Att: 44,901
Ref: Michael Oliver (Northumberland).
Even more impressive was his role in Liverpool's opener after 26 minutes, just as The Kop were starting to get frustrated.
Jonathan Howson took a couple of bites at the Uruguayan but Suarez ploughed on creditably. And when Elliott Bennett intervened with a desperate challenge from the side, the ball went straight to Jordan Henderson, who scored with a sumptuous half-volley.
That opened the floodgates for Liverpool, who must wish they could play Norwich every week having battered them 5-2 at Carrow Road when Suarez grabbed a hat-trick.
This time Steven Gerrard, Sturridge and a Ryan Bennett own-goal also featured on the scoresheet. Sturridge's close-range effort, after goalkeeper Mark Bunn had missed a Stewart Downing cross, meant he became the first Liverpool player since Ray Kennedy in 1974 to score in his first three appearances for the club.
He got a standing ovation when he was taken off with Liverpool already assured of the win that took them to within six points of Spurs in fourth.
Stunner: Jordan Henderson put Liverpool ahead against Norwich at Anfield
'The first goal was the important one,' said Rodgers. 'It is difficult to find space early on but once you go ahead, they have to open up. It was terrific work by Suarez and a great strike by Jordan. Once we got the goal, we controlled the game.'
Having selected Suarez and Sturridge together for the first time, Rodgers could not have been happier, saying: 'Luis has been terrific for us all season but now he has got a recognised goalscorer up beside him, teams have someone else to worry about as well.
'Sturridge not only has pace and power, he's a clever player. They are a very fluid pairing. We have seen it in training.'
Having selected Suarez and Sturridge together for the first time, Rodgers could not have been happier, saying: 'Luis has been terrific for us all season but now he has got a recognised goalscorer up beside him, teams have someone else to worry about as well.
'Sturridge not only has pace and power, he's a clever player. They are a very fluid pairing. We have seen it in training.'
On target: Luis Suarez doubled Liverpol's advantage before half time at Anfield
Norwich boss Chris Hughton saw Ryan Bennett head a chance straight at Brad Jones at 0-0 and admitted: 'Goals change games but we weren't as good as we could have been. This is the only game for quite some time where we have been clearly beaten.'
With Liverpool chairman Tom Werner making a rare visit to Anfield, there was some anxiety from the home fans about the absence of defensive stalwarts Pepe Reina and Martin Skrtel. But Norwich had not won at Anfield since 1994 and never looked like doing so here.
Sturridge started in the middle and Suarez out on the left but they changed so often Norwich did not know how to cope.
With Liverpool chairman Tom Werner making a rare visit to Anfield, there was some anxiety from the home fans about the absence of defensive stalwarts Pepe Reina and Martin Skrtel. But Norwich had not won at Anfield since 1994 and never looked like doing so here.
Sturridge started in the middle and Suarez out on the left but they changed so often Norwich did not know how to cope.
Main man: Daniel Sturridge scored his third goal in as many games as Liverpool ran riot
The interplay between Liverpool's strikers became apparent with the second, 10 minutes later. Lucas threaded a pass to Sturridge from midfield but the striker cleverly let it run through his legs.
Almost by telepathy, Suarez hardly had to break stride to collect the dummy and beat Bunn left-footed.
Jumping for joy: Steven Gerrard celebrates after scoring Liverpool's fourth goal against Norwich
Worryingly for Hughton, they opened up alarmingly in the second half as heads dropped.
Just before the hour, Bunn made a hash of Downing's driven cross and the ball fell kindly to Sturridge, who tapped in. It was the youngster's third Liverpool goal.
There was still time for Gerrard to get in on the act, shooting home from nearly 30 yards with no Norwich defender closing him down.
And the ultimate humiliation was saved until last when substitute Raheem Sterling turned Michael Turner and his cross was then deflected in by Ryan Bennett.
Game over: Norwich's Ryan Bennett looks dejected after scoring an own goal
Five star: Raheem Sterling celebrates after his cross was turned into his own net by Ryan Bennett.
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