Summer additions George Thomas and Sam Hughes found the net for the Foxes in the opening 12 minutes at Glanford Park before a consolation strike from Kevin Van Veen just before the interval.
Up against Sky Bet League 1 opposition, Steve Beaglehole had Kelechi Iheanacho, Leonardo Ulloa, Ben Hamer, Dan Amartey, Yohan Benalouane and Aleksandar Dragović among his side.
Despite making seven changes from the XI who overcame Everton in the Premier League Cup last Friday, Academy graduate Hamza Choudhury remained as skipper alongside Hughes in midfield.
Elsewhere, eight of City's 18-man squad were also beneficiaries of the Club's Academy, giving them a unique chance to play both alongside and against established, professional opposition.
Leicester were on the front foot straight from the first whistle and they took the lead inside three minutes.
Former Coventry City man Thomas intercepted outside the Iron’s box and played it across to Ulloa before the Argentine returned it for him to slide home into the corner.
Scunthorpe themselves made nine changes from a 3-0 defeat by local rivals Doncaster Rovers in the Emirates FA Cup and they initially struggled to handle Beaglehole’s visitors.
City's dominance paid off further after 12 minutes when a fearsome cross from Layton Ndukwu was punched into the air by Rory Watson.
Once it had returned to ground level, Hughes was perfectly positioned to flick it tidily into the back of the net.
Not content with their two-goal advantage, City pressed forward again on the half-hour mark but Ndukwu couldn’t get enough power on his header from Iheanacho’s cross.
When Clayton Lewis broke into a pocket of space in the Foxes box, however, they needed Hamer to be alert to make a strong stop with his left arm to keep out a powerful low drive.
Graham Alexander’s hosts, who sit third in the League 1 standings, were rewarded for their endeavour with seconds remaining of the first half to go.
Their goal came as former PSV Eindhoven trainee Van Veen nodded it beyond Hamer to narrow the arrears, although City had mostly looked assured at the back.
After the break, the play became increasingly bogged down in midfield, but Choudhury and Hughes were a match for their more experienced counterparts.
It was Alexander's Iron who threatened most in the latter stages, though, with Lewis first rattling the woodwork before forcing Hamer into another save with five minutes to play.
The City stopper was called upon at the very end, saving well to keep out a low half-volley from Lewis to seal safe passage for his side.
Major moment
Securing an advantage on the scoresheet so early in the fixture, courtesy of a fine effort from Thomas, settled things down and, once that lead had been doubled, it gave the hosts a mountain to climb.
While their attempts to scale it were admirable, the Foxes ultimately had enough about them to see off the Iron in chilly conditions in Lincolnshire.
Who impressed?
A composed figure in a less familiar role in the centre of midfield, Hughes battled away for the cause in the middle of the park for Begalehole’s visiting Foxes.
The ex-Chester defender helped put City on track to victory, too, with a delicate flick after just 12 minutes to continue his excellent form for the Club’s Development Squad this term.
Where does it leave us?
Safely into the hat for the Round of 16 draw. City will discover their opponents on Friday afternoon when the draw is made at 12:30pm – and you can follow it live on the Club’s Twitter feed.
Coming up…
The Foxes are next in action on Monday afternoon for a 1pm kick-off against Premier League 2 champions Everton at Belvoir Drive, a clash you can watch for FREE on LCFC TV.
Then it’s the visit of Legia Warsaw to Holmes Park on Thursday 14 December (7pm kick-off) in the Premier League International Cup.
The details...
Scunthorpe: Watson, Townsend, Wallace (c) (Burgess 45), Madden (Church 65), Van Veen, Lewis, Redmond, Goode, Sutton, Butroid, Hornshaw.
Subs not used: Kelsey, Morris, Bishop, Holmes, McArdle.
City: Hamer, Amartey, Dragović, Benalouane, Wood, Choudhury (c), Ndukwu (Eppiah 70), Hughes, Thomas (Knight 91), Iheanacho (Muskwe 75), Ulloa.
Subs not used: Iversen, Pascanu, Dewsbury-Hall, Kaba Sherif.
Goals: Thomas 3, Hughes 12.
Referee: Trevor Kettle
Attendance: 824