It was leading marksman Jamie Cureton who came off the bench to win it for the Canaries.
He struck in the 78th minute with a shot that went in off a post after a surging run forward by full-back Jon Otsemobor had opened up the home defence.
Earlier Darren Huckerby had squandered a couple of golden second-half opportunities for Norwich.
First he blasted a clear-cut chance high over the top and then he forced his way unmarked into the box to fire in an effort that was blocked by goalkeeper Joe Murphy.
Murphy had rescued Scunthorpe in the first half with a couple of good close-range saves to deny striker Ched Evans, on loan to the Canaries from Manchester City.
But Scunthorpe played their part in a hard-fought game with former Carrow Road junior Paul Hayes just inches away with a cracking volley.
Martin Paterson went close for the home side with a close-range effort that was blocked away by the legs of goalkeeper David Marshall.
And when Scunthorpe did get the ball in the back of the net early in the second half, through striker Jonathan Forte, he was unlucky to see it ruled out for offside.
The home side battled right to the very end and, in stoppage time, came within a whisker of an equaliser when a curling effort from Paterson was turned away at full stretch by goalkeeper Marshall.