Takumi Minamino scored twice and Divock Origi grabbed the other goal as Liverpool progressed to the Carabao Cup fourth round with a 3-0 victory at Carrow Road.
Minamino pounced on Divock Origi's knock-down from a corner to fire a heavily-rotated Reds XI in front after just four minutes.
The hosts grew into the first half and should have drawn level via the penalty spot after Conor Bradley fouled Dimitris Giannoulis, but Christos Tzolis saw his effort denied by Caoimhin Kelleher.
With teenagers Conor Bradley and Kaide Gordon forming Liverpool's right side, Jurgen Klopp handed another youngster his debut as by introducing Tyler Morton for Naby Keita at half-time.
Liverpool were once again most threatening at the start of the half and Origi doubled the lead in the 50th minute by glancing Kostas Tsimikas' cross beyond Angus Gunn.
The Belgian striker could have had a second moments later as he brushed just wide of the far post.
Instead it was Minamino who doubled his tally by finishing under Gunn following Alex Oxlade-Chamberlain's through-ball to cap an excellent evening for Liverpool's fringe stars.
Here are five talking points from the Carabao Cup clash.
1. Kelleher steals show for Reds
Caoimhin Kelleher denied Christos Tzolis' poor effort from 12 yards
Whether it was surging out of his box to shut down danger behind a high defensive line or his crucial penalty save, Caoimhin Kelleher produced what was arguably his finest performance in a Liverpool shirt against Norwich City.
The 22-year-old was equal to every effort which came his way, including Christos Tzolis' tame penalty down the centre of the goal, which he managed to save with his feet despite diving to his right.
The confidence of Liverpool No.1 Alisson is clearly rubbing off on Kelleher, who also caught the eye with his brilliant sweeping.
Twice the Republic of Ireland international made powerful headers to clear danger from outside his box, while he was not afraid to clean out his own teammates to clear the danger.
2. Minamino seizes chance
Takumi Minamino scored an important goal to put Liverpool in front
Heavy rotation, an away tie and midweek fatigue.
These have been Liverpool's downfall in domestic cup ties in recent years, so Takumi Minamino's early strike was just what the Reds needed Carrow Road.
The Japan forward latched onto Divock Origi's knock-down after a corner to sweep into the far corner in the fourth minute, giving a youthful Liverpool outfit the nerve-settling goal they needed.
It could prove to be an important strike for Minamino, who knows goals must be the currency he deals in to force his way into Jurgen Klopp's plans.
The 26-year-old was an unused substitute in five of Liverpool's six previous games - he was injured for the sixth - but his pressing, creativity and eye for goal prove he belongs at Anfield and will have a part to play this season.
3. Konate backs-up debut showing
Liverpool may not have had a busy transfer window, but their sole signing is already looking like shrewd business.
Ibrahima Konate partnered Virgil van Dijk to keep a clean sheet on his Reds debut, the 3-0 win over Crystal Palace on Saturday, and followed that up with another shutout alongside Joe Gomez against Norwich City.
The former RB Leipzig man oozes confidence stepping out with possession and distributing, while his dominant frame makes him a regular threat from set pieces, as shown when he headed over from a corner in the 13th minute.
Norwich City did pose some threat and, of course, they should have drawn level from the penalty spot, but Konate and Gomez can be pleased with their joint performance on their first outing together.
Gomez - Liverpool's captain on the night - also deserves a special mention for his seamless return to action since returning from the major knee injury he suffered last November. The Englishman's best moment came when he cleared the danger in the immediate aftermath of Kelleher's penalty save.
4. Verdict on Liverpool's youthful right side
Conor Bradley was defensively sound until his lapse of concentration to concede the penalty
If you added up the exact ages of Liverpool's right side of Conor Bradley (18) and Kaide Gordon (16), they would be very similar to that of 35-year-old James Milner.
Reds veteran Milner lined up at right-back against Crystal Palace but he was unavailable to face Norwich City due to waking up with a cold, Jurgen Klopp confirmed ahead of kick-off.
This paved the way for Bradley to line up at right-back behind right-winger Gordon, who became Liverpool's fifth-youngest player by featuring against Norwich City.
Both teenagers looked at home on the big stage for most of the match and there were plenty of bright dribbles in the Canaries half.
That being said, Bradley will be disappointed with the clumsy nature of his tackle on Dimitris Giannoulis, although he was bailed out by Caoimhin Kelleher and he is sure to learn from the experience.
5. Tsimikas keeps up brilliant start to season
Kostas Tsimikas provided the assist for Divock Origi's header
Kostas Tsimikas has been a revelation for Liverpool of late.
The Greece international hardly had a look in last season but he was called into action this campaign due Andy Robertson's injury last month.
Tsimikas kept back-to-back clean sheets in the Reds' first two Premier League games, grabbing an assist, and Jurgen Klopp clearly feels he can trust the left-back, as he showed by starting him against Crystal Palace.
The 25-year-old kept his place in the XI for the trip to Norwich City and he, like Robertson so often is, was a key attacking outlet for Liverpool down the left. He thoroughly deserved his assist as he picked out Divock Origi with a cross early in the second half.
Understandably, Tsimikas was the more solid of the Liverpool full-backs on the night and he was one of the Reds' standout performers before Robertson replaced him on 66 minutes.
6. Liverpool engine room shows gulf in quality
Alex Oxlade-Chamberlain helped Liverpool win the midfield battle
For much of the match, Liverpool's midfield trio of Alex Oxlade-Chamberlain, Naby Keita and Curtis Jones were consigned to doing the hard, unglamorous work.
Three tireless and positionally-aware operators in the centre of the park may have been just what the Reds needed to batter Norwich City into submission.
It took a while for the trio to extend themselves, with Oxlade-Chamberlain outshone on set-piece delivery by Kostas Tsimikas and Jones suffering a couple of sloppy moments in the first half.
But they had the chance to show off their full quality as Norwich tired in the second 45 miinutes, with Keita and Jones weaving through tight spaces to drive the team forward from midfield.
Oxlade-Chamberlain, meanwhile, nudged the ball through to Takumi Minamino to earn an assist in the 80th minute.