But the Potters battled back and denied the home side a much-needed victory with two second-half goals - Lee Mills' spectacular equaliser hitting the net just three minutes from full time.
In the second minute of the game Malky Mackay headed goalwards at the far post from Mark Rivers' left-wing corner.
Paul McVeigh played the loose ball back to David Healy and when his shot was blocked on the line by Marcus Hall, Roberts stooped to head home from close range.
The visitors recovered from this early setback and put together some promising moves without managing to get a shot on target.
In the 21st minute Norwich were forced to make a substitution, the injured Adam Drury being replaced by Chris Llewellyn.
Mackay put the home side two up in the 23rd minute with a powerful header from Darren Kenton's right-wing cross.
Once again Stoke responded by forcing Norwich on tto the defensive for long periods and in the 37th minute Brynjar Gunnarsson brought a good save from Robert Green with a rasping left-foot drive.
In first-half stoppage time Healy was unlucky to see his header rebound off the crossbar.
Three minutes into the second half Chris Iwelumo limped off to make way for Lee Mills.
Healy was denied a debut goal when Steve Banks saved with his legs - a save that proved to be crucial.
In the 62nd minute Gunnarsson gave Green no chance with a near post header from Peter Hoekstra's left-wing cross.
McVeigh brought a save from Banks and Green did well to keep out a fierce shot from Frazer Richardson.
Rivers made way for Keith Briggs to make his Norwich debut before Mills conjured up a stunning shot, his 20-yard left-foot strike curling inside Green's left-hand post.