Stoke looked the more dangerous side throughout and, in the 27th minute, John Eustace squeezed the ball through to Chris Greenacre on the right who swung the ball over to Gifton Noel-Williams but his shot was miscued and flew over the crossbar.
Stoke's pressure finally paid off in the 36th minute and when new boy Ade Akinbiyi got past Craig Fleming on the edge of the box he crossed for Noel-Williams who neatly chipped the ball over the keeper from six yards with Adam Drury trying in vain to clear off the line.
Substitute Phil Mulryne made an instant impact as the Canaries came out for the second half looking a lot sharper.
They eventually hit the target in the 67th minute when Darren Huckerby received the ball on the left side of the six-yard box and, despite pressure from Eustace, he struck his shot past Ed de Goey.
Ten minutes later, it was Mulryne again who inspired the Canaries and his superb 25-yard free kick fully tested de Goey but Fleming was left disappointed when he sent the rebound rocketing over an empty net in to Row Z.
Norwich manager Nigel Worthington said after the game: "We knew Stoke were going to come at us. There was a lot of sloppy passing in the first half but Phil (Mulryne) came on later and settled the whole team.
"On another day there could have been more goals but all in all it's been a good week's work."
Stoke: de Goey, Thomas, Williams, Marcus Hall, Russell, Eustace, Andrews, Clarke, Greenacre, Noel-Williams, Akinbiyi. Subs: Cutler, Iwelumo, Neal, Commons, Hoekstra.
Norwich: Green, Edworthy, Fleming, Mackay, Drury, Harper, Francis, Holt, Easton, Huckerby, Crouch. Subs: Mulryne, Roberts, Crichton, Notman, McVeigh.
Referee: P Joslin (Nottinghamshire).