Liam Lawrence wasted an early opening for Stoke when he fastened on to a pass from Ricardo Fuller. But Darren Huckerby was more clinical for the visitors when he fired them ahead in the fifth minute.
Dion Dublin outwitted Leon Cort to head the ball on and Huckerby out-paced Stephen Wright before smashing his shot past Steve Simonsen.
Stoke came back strongly as Mamady Sidibe's header forced a flying save from David Marshall and a cross from Lawrence just evaded the on-rushing Fuller.
But veteran Dublin, who gave a master-class of old-fashioned centre-forward play in the first half, almost doubled Norwich's lead from Mo Camara's cross.
Back came Stoke with Marshall clutching Lawrence's shot back from the goal-line and Fuller beating Jason Shackell to drill his shot inches too high.
And City deservedly drew level 30 seconds after the break when Lawrence whipped in a cross for Cort to bury a well-placed header.
Stoke felt they should have had a 53rd minute penalty when Gary Doherty blocked Fuller's volley with his hands and Pulis was sent to the stands for his heated protest.
But the home side were now rampant and Fuller pulled his shot wide from a tight angle after excellent work by Danny Pugh, before Cresswell almost finished off a long throw from Rory Delap.
The chances continued with Cort heading wide from a cross by Ryan Shawcross before Cresswell blazed over with the goal at his mercy.
Fuller had another effort saved before the winner finally arrived. Lawrence's corner was headed down by Cort and Cresswell hooked the ball in from point-blank range.