Simon Lappin's first Norwich goal for five years helped Chris Hughton pick up his first win as Canaries manager.
Lappin gave the hosts the lead against Scunthorpe, firing in from 25 yards.
But the League One visitors forced their way back into the League Cup tie when Mark Duffy rifled an equaliser before half-time.
Norwich secured victory when Wes Hoolahan scored from the penalty spot after he had been fouled by Niall Canavan.
It was far from comfortable for Hughton and his players but it was a case of job done for the Premier League club.
The Canaries had managed to establish a level of dominance by the half hour mark and were rewarded with the opening goal in the 32nd minute.
Andrew Surman played a pass in-field to Lappin and he took a touch before rifling a powerful drive past Sam Slocombe in the Scunthorpe goal.
Alan Knill's side have lost all three of their League One games so far this season but they did not let their heads drop and were level two minutes later.
Christian Ribeiro picked out Duffy, who curled in an effort from 30 yards that went in off the inside of the post.
But Norwich advanced to the third round after Hoolahan was brought down in the area by Canavan, the Canaries skipper picking himself up to find the net from the spot in the 56th minute.
Norwich City 13 Rudd 06 Turner 23 Tierney 24 R Bennett 33 Francomb 11 Surman 14 Hoolahan 15 Fox 26 Lappin (Pilkington - 52' ) 16 Morison (Jackson - 80' ) 25 C Martin Substitutes 01 Ruddy 02 R Martin 20 Barnett 04 Johnson 12 Pilkington 09 Holt 10 Jackson Scunthorpe United 01 Slocombe 02 Ribeiro 05 Mirfin 15 Canavan 21 Newey 04 Walker (Prutton - 66' ) 07 Ryan 14 Gibbons 16 Duffy 10 Grella (Jennings - 80' ) 11 Barcham (Grant - 80' ) Substitutes 13 Severn 20 Howe 18 Hughes 24 Prutton 09 Grant 12 Jennings 23 Keegan
Ref: Phil Gibbs