The Canaries' 18-year-old striker Adam Idah netted a hat-trick in a game which Lilywhites keeper Connor Ripley won't look back on with any fondness.
Ripley was at fault for the visitors' second and third goals, while he also conceded the penalty for the fourth when Idah was clear on goal.
Idah took less than 90 seconds to put his side in front, running through to steer a shot past Ripley.
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Ripley allowed an Onel Hernandez shot to go under his body in the 28th minute, then side-footed a clearance straight to Idah who lifted a shot over him from 40 yards to make it 3-0 six minutes before half-time.
Billy Bodin reduced the deficit three minutes into the second half with a close-range header but Idah completed his hat-trick from the penalty spot just after the hour-mark.
Josh Harrop scored a late consolation to give the scoreline slightly more respectability and a final flourish saw Bodin twice denied by keeper Michael McGovern.
Ben Davies and Darnell Fisher were the only two players to start this game and the New Year's Day defeat to Middlesbrough.
North End lined-up in a 4-2-3-1, Tom Bayliss and Ryan Ledson in the central midfield roles, with Brad Potts playing as the No.10.
Billy Bodin operated on the right-wing and Josh Harrop on the left.
They were chasing the game from inside the first 90 seconds as Norwich nosed in front and never looked back.
Jamal Lewis' pass was picked up by Marco Stiepermann who motored unchallenged through midfield before sending Idah through on the goal, the Irish teenager steering a first-time low shot past Ripley into the far bottom corner from the edge of the box.
With a quarter of an hour gone, Davies' cross was nodded down by Jayden Stockley into the path of Fisher, his low shot forcing a diving save from McGovern.
Stockley then headed wide at the far post after meeting Joe Rafferty's fine cross from the left channel.
Bodin couldn't get any power in his shot when a pass from Bayliss deflected into his path on the edge of the box.
Those chances came in a little spell of pressure for North End but any signs of them getting back into the game were taken away by two more Norwich goals in the space of 10 minutes.
In the 28th minute, Ripley had just saved from Idah in a one-on-one with the ball picked up Hernandez down the left channel.
Hernandez cut inside on to his right foot and hit a low shot which went under the body of the diving Ripley and into the net
If that wasn't bad enough for the keeper, he was culpable for the third too in the 38th minute.
Ripley dashed out of his box to reach a through ball ahead of Hernandez but instead of putting it into row Z, side-footed the ball straight to Idah 40 yards out.
Idah still had work to do and he returned a superb first-time finish back over the stranded Ripley and into the roof of the net.
Words - and probably many unprintable ones - were no doubt said in the dressing room at half-time and North End started the second half strongly.
It brought them back into the contest, briefly, as they reduced the arrears in the 48th minute.
Bodin tried his luck with a shot from 25 yards which was straight at McGovern but was fumbled by the keeper and turned behind for a corner.
Harrop delivered the flag kick from the right, Stockley rose to head it goalwards and Bodin nodded it into the roof of the net from three yards.
In the 55th minute, Ledson had a shot from 20 yards after slipping his marker, McGovern diving to his right to parry away at full stretch.
Any hope of an unlikely comeback were dashed on the hour mark when the visitors got their fourth goal from the penalty spot.
There was a strong suspicion of offside when Idah ran clear on to a through ball, Ripley taking him to ground as he tried to take it past the keeper.
Ripley was shown a yellow card by referee Martin Atkinson, Idah stepping-up to complete his hat-trick from the spot.
The keeper got down low at the near post to parry Mortitz Leitner's shot in the 73rd minute and later blocked a close-range from Hernandez.
In between those two chances, an opportunity came North End's way at the other end.
Bodin came inside off the right-wing, side-stepped a challenge in the box and hit a shot which deflected off a Norwich player and looped over the bar.
With six minutes left North End pulled a goal back through Harrop, and a well-worked effort it was too.
Ledson got possession on the left and played a nice ball into Bodin's feet on the corner of the box.
Bodin turned and played in Harrop behind the Norwich back line, Harrop shooting past McGovern.
It led to a late flourish from PNE and they almost scored a third goal in the 89th minute.
Bodin's low shot was pushed out by the diving McGovern, Bayliss getting to the rebound first but seeing his effort blocked by the keeper.
McGovern again denied Bodin in stoppage-time, parrying his shot with Rafferty slicing the follow-up across the box.
PNE: Ripley, Fisher, Storey, Davies, Rafferty, Ledson, Bayliss, Bodin, Potts, Harrop, Stockley. Subs (not used): Pearson, Clarke, Gallagher, Barkhuizen, O'Reilly, Nugent, Rudd.
Norwich: McGovern, Byram, Zimmermann, Amadou, Lewis, Leitner, Trybull (Hanley 68) Stiepermann, Cantwell (Aarons 81), Hernandez, Idah (McLean 85). Subs (not used): Vrancic, Buendia, Tettey, Krul.
Referee: Martin Atkinson (West Yorkshire)
Attendance: 7,616 (833 away)