The Canaries dominated the game from start to finish, yet had to bounce back from falling behind to a early strike from Gary Birch.
But goals from Ian Henderson, Paul McVeigh and on-loan striker Peter Crouch sealed their success and left the Norwich boss Nigel Worthington purring.
The only sour note for Norwich was the dismissal of Crouch after a last minute bust-up with Walsall central defender Paul Ritchie who also saw red.
Worthington said: "The goals we scored must be three of the best that I have seen since I have been at the club.
"It was a fantastic performance and one that we can build on. Even when we fell a goal behind I was always confident that we would come back into the game."
Walsall were seeking a fourth straight home win and manager Colin Lee said: "Norwich have got to be the best team we have played against this season.
"There were aspects of our play I was pleased with, but we gave the ball away too cheaply.
"We also lost out discipline after Ritchie was sent off and that is something I will not stand for."
Substitute Henderson fired Norwich level after 52 minutes when he turned home a cross from Adam Drury following a neat pass from McVeigh.
It was a blow that Walsall did not recover from and McVeigh effectively sealed their success eight minutes later.
Darren Huckerby and Crouch combined to set up McVeigh who gave Walsall goalkeeper James Walker no chance from close range.
Crouch then set the seal on City's impressive display with a simple tap in from close range after a cross from Henderson.
Walsall, who had survived an early scare when Walker had to tip away a 25-yard drive from McVeigh, stunned City when Birch struck after nine minutes.
City failed to clear a cross from Simon Osborn and when Jamie Lawrence nodded the ball down to Birch he muscled his way past Drury before firing into the roof of the net from eight yards.
Birch's second goal of the season signalled an intense spell of City pressure - but Walker stood firm.
He denied Damien Francis with another smart save after 14 minutes and when City did find a way past him they were denied by the woodwork.
Phil Mulryne whipped in an 18th minute free-kick from 25 yards only to see his shot crash off the top of the bar.
On-loan Crouch then squandered two golden chances to equalise when he twice headed wide from close range.
Ironically, having been penned in their own half for so long, Walsall could have doubled their advantage in a rare attack ten minutes before half-time only to be denied by City keeper Robert Green.
Green did well to push a fierce 30-yard drive from Vinny Samways over the bar before City launched their decisive second-half goal blitz.