City were held to a draw at the Bet 365 Stadium despite taking the lead twice.
Onel Hernandez was the first name on the scoreboard after drilling home a low effort 24 minutes in, but Ashley Williams headed the Potters level just after the break bringing them back into the game.
A Teemu Pukki header then gave City hope with less than 30 minutes to play, but again Stoke found the equaliser to hold Norwich to their fourth draw on the spin.
Daniel Farke made just one change to the starting eleven who faced Sheffield Wednesday on Friday, with Emi Buendia returning from suspension in place of Moritz Leitner.
Norwich made a great start and won a corner within the second minute. Buendia’s ball into the box was cleared away but only as far as Onel Hernandez who hit a low strike from 18-yards, but it went just narrowly wide of the post.
Moments later Kenny McLean nodded the ball down into space for Marco Stieperman who had a shot from outside the box, but it went well over.
Ten minutes in and a brilliant chance fell for the Potters with Sam Clucas getting on the end of a good cross from Tom Edwards, but he could only head it over at the back post.
Norwich then won a free-kick in the Stoke half which was taken by Buendia. His ball was headed backwards by a Potters’ defender, falling nicely for Pukki to power it towards goal with another header, but Jack Butland made a great save from close range with his feet.
The Canaries took the lead with 24 minutes on the clock as Jamal Lewis crossed the ball into the box. It deflected off a Stoke defender and fell back to Hernandez who struck a powerful shot into the bottom left corner.
Stoke tried to look for an equaliser with Peter Etebo hitting an ambitious attempt from 30 yards out, but it flashed wide of City’s right-hand post. James McClean then looked to get away on the right, but Max Aarons did a superb job racing back to get in a sliding block before his cross could go in.
Stoke made a good start after the break and soon got the equaliser. Aarons made a crucial block again to deny Afobe a shot at goal, however the resulting corner fell to Ashley Williams who headed past Krul at the back post. The City keeper got a hand to it but couldn’t divert it from goal.
The Potters continued to ramp up the pressure, with Thibaud Verlinden shooting from distance, but Krul comfortably made the save. Etebo then had a decent effort from 30 yards, but again Krul got his hands to the ball.
Farke made his first substitution in the 54th minute, with Mario Vrancic replacing Tom Trybull.
A brilliant chance came for Stoke just past the 60-minute mark with Norwich unable to clear away from danger. The ball was put back into the box where Clucas got a touch, but he could only fire it over the bar.
City took the lead again 66 minutes in as Vrancic lifted a lovely ball over the heads of the Stoke defence for Teemu Pukki to nod past Butland.
However, the celebrations were short-lived, with a second goal from the Potters three minutes later. Tom Edwards got the equaliser with a low strike just pas Krul’s reach.
Edwards was substituted in the 80th minute after picking up a knock and was replaced by Nathan Collins.
The Canaries then made their second change, with Leitner coming on for Hernandez.
City were desperately searching for the winner and came close with a good run from Lewis down the left. He got a shot away from an angle, but it rolled just wide.
Five minutes of additional time was played, with Norwich continuing to go for goal but they were unable to make any of their chances count.