City picked up their second consecutive victory at the Britannia Stadium after Richard Cresswell fired in a late winner.
The former Preston man was on hand to divert Leon Cort's header in to the back of the net with just two minutes remaining.
Darren Huckerby put the visitors 1-0 up after just six minutes, before Cort levelled the scorelines straight after the half time interval.
Tony Pulis fielded an unchanged side ahead of the clash, after Stephen Wright past a late fitness test.
The Potters started the match with a good tempo and it took less than a minute for Liam Lawrence to make a strong run down the right, cut inside and play a good ball across the area, just avoiding Richard Cresswell coming in from the left wing.
Then after just six minutes the Canaries hit the Potters on a counter attack to take the lead.
A long ball played up the field was expertly flicked on by veteran Dublin, into the path of Huckerby, who held of Stephen Wright before firing a powerful finish home.
Dublin found himself at the centre of the action at the other end on eleven minutes.
Creswell from the left, swung in a dangerous ball, which came of the head of Dublin and straight toward the goal.
It was only a great save from Marshall to deny Stoke an equaliser.
On 22 minutes Lawrence put over a dangerous in swinging free kick from the left, which had the Norwich defence panicking only for the ball to be put out for a corner.
Just after the half hour, on loan Sunderland man Wright was replaced by Andy Wilkinson, after complaining of an injury.
Lawrence was again at the heart of things on 35 minutes. Delap's rocket throw had the Norwich defence at sixes and sevens and Lawrence, who was always stretching for the chance, saw his shot saved on the line by David Marshall.
Then on 40 minutes, just before half time Ricardo Fuller had his first chance of the game.
However, he fired just over the bar, with a powerful effort, after good work in midfield by Delap and Eustace.
The second half had hardly started, after a good cross from the left by Danny Pugh was glanced in by Leon Cort.
It was a wonderful ball from Pugh, coolly put away by the big man.
Stoke had two strong cases for a penalty turned away by referee Lee Probert.
Both looked to be good shouts and the City boss clearly felt hard done by, as he was harshly sent to the stands for remonstrating with the referee from Wiltshire.
Fuller was also booked for simulation after a challenge just inside the box in the 58th minute.
The sixty third minute sees Norwich's first chance of the half, with Dublin failing to connect properly with a low hit cross from the left hand edge of the penalty area
A minute latter it was almost 2 -1 to the Potters; Fuller's flick, bought Cresswell into the game and it was more through luck than judgement that Marshall managed to keep the striker's header out.
Cort went close again in the final stages of the game, but just as a draw looked the most likely outcome, Cresswell was on hand to power in from close range, much to the delight of the 18,000 City supporters.
