The Uruguayan became the first player in Premier League history to score three hat-tricks against the same opposition, while Raheem Sterling added a late fifth for the hosts
The Uruguayan has now scored 11 in his last four appearances against Norwich, with this being his third treble in that time, and three of the strikes were of the highest quality.
The opener came after quarter of an hour as he thumped in a long-distance volley, before turning home a corner 14 minutes later.
His third was a beautifully struck half-volley from the edge of the box as he became the first Premier League player to score three hat-tricks against the same side, before he netted his fourth with a curling free kick 15 minutes from time.
|VIEW FROM ANFIELD
|By Tom Maston at Anfield
"One name was on everyone's lips at Anfield after Luis Suarez lit up a chilly evening in Liverpool. The Uruguayan was simply unstoppable as he scored four, including three Goal of the Season contenders.
"Anyone who doubted he would miss strike partner Daniel Sturridge were certainly put to rights by this showing, though tougher defences than that of Norwich City will face up to the striker in the coming weeks. For now, however, he looks unstoppable."
Liverpool made three changes from the side that lost to Hull City, while Norwich had just one alteration from the weekend as Johnson replaced Gary Hooper.
It was the home side who started on the front foot and Suarez gave the Reds the lead in spectacular fashion after 15 minutes.
John Ruddy made poor contact with a goal-kick and, as the ball bounced in favour of the Uruguayan, he looped a first-time volley high over the goalkeeper and into the back of the net from 40 yards.
And Suarez doubled the advantage in the 29th minute, hooking home Philippe Coutinho's left-wing corner after being given too much space six yards from goal.
Six minutes later, the striker completed his treble with another stunning strike.
After receiving the ball from Sterling, Suarez drove forward, chipped the ball around Leroy Fer and sent a searing half-volley beyond Ruddy from 20 yards to cap an exhilarating first-half performance.
Sebastien Bassong sent a free header over the crossbar four minutes after the break but two minutes later it almost got worse for Norwich as Ryan Bennett had to clear Steven Gerrard's goalbound header off the line.
Joe Allen was next to threaten the visitors' goal, bringing a flying save out of Ruddy with a thumping effort from 25 yards, before the England international dived low to his left to deny Suarez.
But Suarez did grab his fourth with a perfect 20-yard free kick that curled beyond the despairing Ruddy into the top corner, before Gerrard fizzed an effort of his own narrowly wide of the post.
In a frantic finish, Johnson flicked home Nathan Redmond's cross eight minutes from time, Gerrard hit the post and Sterling converted Suarez's pass as Liverpool bounced back from Sunday's humbling defeat to Hull City in style.