After Peter Thompson had fluffed a great early chance for Stockport, the visitors went in front after 16 minutes. Goalkeeper Owain Fon Williams completely missed Simon Lappin's in-swinging free-kick, allowing Grant Holt to head home easily from six yards.
Norwich were buoyed by their goal and both Adam Drury and Darel Russell came close to doubling their advantage before the interval.
Stockport responded when Michael Rose went on a mazy run before scooping a shot just over the crossbar.
Norwich went two up courtesy of a spot-kick on 69 minutes. Chris Martin went down following a clumsy challenge from Paul Huntington, and up stepped Wes Hoolahan who just beat the outstretched arm of Fon Williams.
Stockport forced a frantic finish when they got one back with nine minutes left, with Carl Baker's shot going in off the backside of the offside-looking Thompson.
However, Holt wrapped up a deserved win with a 90th minute tap-in.