The scoring in the Capital One Cup second round defeat at Carrow Road was opened by home midfielder Simon Lappin, with a thunderous low drive on 32 minutes.
However, Mark Duffy equalised in spectacular fashion himself just two minutes later as his volley cannoned in off the post.
Nevertheless, the hosts found the match-winner early in the second half as Wes Hoolahan was brought down by Niall Canavan, as the midfielder stepped up to slot home the subsequent penalty.
The Iron made two changes for the game. Andy Barcham came in for Bobby Grant in the side, while toe injury victim Callum Kennedy was replaced from the team which lost to Yeovil Town on Saturday by Tom Newey.
Sam Slocombe started in goal, with Christian Ribeiro, David Mirfin, Niall Canavan and Newey forming the defence.
The midfield consisted of Duffy, Josh Walker, Robbie Gibbons, Jimmy Ryan and Barcham, while Mike Grella led the attack.
The substitutes were James Severn, Grant, Connor Jennings, Mark Hughes, Callum Howe, Jordan Keegan and David Prutton, who signed from Sheffield Wednesday on a three-month loan earlier in the day.
The first chance of the night came Scunthorpe's way on three minutes when Duffy drove forward and played Barcham in down the left, who cut into the penalty area and drilled a shot towards goal which Declan Rudd had to be alert to tip out. The ball was then cleared before it reached the onrushing Grella.
And end-to-end-start continued as Wes Hoolahan's drive was deflected wide of goal for the hosts just a minute later.
In the 14th minute, the hosts were presented with a further chance when Martin connected with a Fox cross but sent his effort wide.
As the half wore on, the hosts continued to have the better of the possession but it would prove to be an opening period of few chances,
The away team came close to creating a chance midway through the opening period as Ryan's volleyed cross from the right-hand side just missed the head of Grella and drifted wide.
And the hosts soon too the lead as, on 32 minutes, Lappin let fly with a fizzing effort from the edge of the 18-yard box which flew into the back of the net, beating Slocombe at his bottom left-hand post.
However, just two minutes later, Scunthorpe levelled in spectacular fashion when Duffy received the ball on the edge of the area and let fly with a stunning left-footed effort which crashed into the net off the post.
In the 38th minute, the hosts almost regained the lead as Ryan Bennett got on the end of a right-wing corner and pounced to send a header just wide of Slocombe's bottom right-hand post.
The second half got off to a slow start with both sides feeling their way back into the game, but Norwich were handed the chance to go back ahead in the 55th minute when Hoolahan was felled in the penalty area by Canavan.
The midfielder then stepped up to slam his penalty into the top corner and beyond the despairing dive to the left of Slocombe.
Scunthorpe tried to find a way back into the game, with Duffy enjoying some success attacking from the right and cutting inside, but chances were still at a premium against their Premier League opponents.
Gibbons' inwswinging free-kick was cleared to safety before Duffy played Grella through down the right of the penalty area, but his clipped effort from an acute angle was palmed away for a corner by Rudd.
After that set-piece was only part cleared, Barcham then turned to drill an attempt towards goal which Rudd had to get down quickly to stop.
The visiting side continued to try and force the initiative, and Walker was next to have an attempt - this one driving over the crossbar from 30 yards before being replaced by Prutton for his Iron debut.
However, the home side soon seemed to gain a head of steam and stepped it up another couple of gears - threatening through Hoolahan, and then Morison, whose header drew a stop from Slocombe.
Prutton made Rudd's hands sting on 79 minutes with a superb volley heading for the top left-hand corner, which the Norwich custodian dealt with in sensational fashion, tipping over the crossbar.
With around ten minutes left, there was a double Iron change as Barcham was replaced by Grant and Jennings came on for Grella.
The Iron kept up their attempts to find an equaliser and Ribeiro saw his curled cross from the right flank just evade Grant, as well as the far post.
There were five minutes of stoppage time but United, who kept putting crosses into the box and pressed the Norwich defence, couldn't find that elusive leveller.
Scunthorpe are next in action on Saturday when they visit Hartlepool United in League One.
Norwich City: Rudd, Turner, Surman, Hoolahan, Fox, Morison (Jackson, 79), Tierney, Bennett, Martin, Lappin (Pilkington, 50), Francomb.
Substitutes not used: Ruddy, Martin, Johnson, Holt, Barnett.
Scunthorpe United: Slocombe, Ribeiro, Mirfin, Canavan, Newey, Duffy, Walker (Prutton, 66), Gibbons, Ryan, Barcham (Grant, 79), Grella (Jennings, 79).
Substitutes not used: Severn, Hughes, Howe, Keegan.