The Uruguayan striker needed just 34 first-half minutes to smash his hat-trick and added his fourth goal with a spectacular 74th-minute free-kick as Liverpool rampaged back to form.
It was his third hat-trick against Norwich in the last four clashes between the sides and the first time in Premier League history any player has bagged three trebles against the same team.
Suarez lifted his total for the season to 13 goals and proved there is life in Liverpool’s Champions League challenge without injured SAS strike partner Daniel Sturridge.
Liverpool had looked nervy in the opening exchanges, but they soon settled, in the 15th minute, when Suarez broke the deadlock in devastating fashion. Norwich goalkeeper John Ruddy would have been disappointed with a goal-kick that made it only as far as Martin Skrtel. When the centre-half headed the ball straight back towards the Kop end, Suarez allowed it to bounce twice before taking it in his stride to smash a 35-yard right-footed shot past Ruddy.
Suarez’s second goal, on 28 minutes, was equally as clinical, although this time he delivered the final blow with his left foot after swivelling just inside the six-yard box to meet Coutinho’s corner.
Anfield was positively buzzing just six minutes later when Suarez returned to his right foot to claim the hat-trick. The striker had made Leroy Fer look leaden-footed when he flicked the ball over him on the edge of the box and then drilled his shot low across the box and in at Ruddy’s left-hand post.
The rest of the half passed in almost stunned silence as it seemed the crowd struggled to take in the sheer brilliance of Suarez’s virtuoso 34-minute performance.
Liverpool continued to press after the restart and could have added a fourth in the 51st minute when Steven Gerrard stooped to head a cross goal-bound, but Ryan Bennett cleared off the line.
It was one of those evenings when the Norwich players would have just wanted to get the game over with as quickly as possible. But Suarez was not finished with his hunt for goals, trying to squeeze one in for an acute angle in the 63rd minute, but it drifted inches wide of Ruddy’s right-hand post.
He finally added his fourth, in the 73rd minute, stepping up to curl a 25-yard free-kick right-footed over the Norwich wall and beyond Ruddy’s dive into the top left corner.
Norwich pulled a goal back in the 83rd minute when Bradley Johnson glanced a header from a deep cross beyond helpless Liverpool goalkeeper Simon Mignolet.
Sterling had done little all evening, but pounced from close range in the 88th-minute for Liverpool’s fifth goal.
LIVERPOOL: Mignolet 6; Johnson 7, Skrtel 6, Agger 6, Flanagan 6 — Henderson 7 (Alberto 68 mins, 5), Gerrard 7, Coutinho 7, Allen 6, Sterling 7 — Suarez 9 (Aspas 90 mins).
NORWICH CITY: Ruddy 5 — Martin 5, Bennett 6, Bassong 6, Olsson 5 — Hoolahan 4 (Murphy 61 mins, 4), Howson 5, Fer 5 (Whittaker, 71 mins, 4), Johnson 5, Redmond 5 — Elmander 5 (Hooper 68 mins, 4).
Referee: Anthony Taylor 7.