The starting line-up for City's youngsters included just a single change from Wednesday's 3-0 win at Doncaster Rovers in the Leasing.com Trophy.
In came Croatia defender Filip Benković for Ghana's Daniel Amartey, as Leicester also shifted from a 5-3-2 system into a 4-2-3-1 stratagem in Whetstone.
Leicester started the better and were unlucky not to take an early lead as they proceeded to carve out three decent opportunities in the opening half an hour.
Callum Right dragged an effort just wide, while George Hirst headed over bar and Luke Thomas sent a low drive into the side netting from an acute angle.
On 35 minutes, meanwhile, Zimbabwe international Admiral Muskwe was felled in the area and stepped up himself to take the spot kick for the in-form Foxes.
Toffees shot-stopper Nico Hansen, though, guessed right and was even able to smother the City striker's effort, aimed at the bottom left corner, and it remained goalless.
After the break, Leicester ensured their dominance was felt on the scoresheet on 58 minutes when George Thomas' corner eventually landed for Muskwe to instinctively finish.
Inside 60 seconds of the restart, it was 2-0 to the Foxes too as Wright got on the end of a Mitch Clark cross to send it soaring into the top corner for the home side.
While the hosts did get one back in the latter moments, courtesy of an Anthony Gordon penalty, it was Leicester who emerged victorious - for the eighth time in a row in all competitions.
Major moment
Two minutes of scintillating football ultimately won it for the Foxes in Whetstone as Admiral Muskwe and then Callum Wright sent Leicester en route to an eight consecutive victory.
Wright's finish in particular was an excellent demonstration of the young City winger's talents and gave his side enough to ride out Anthony Gordon's late spot-kick.
Who impressed?
Speaking live on LCFC TV, former Leicester City manager Micky Adams said: “You could argue cases for Hirst and Thomas, but the one who I thought really did well on the ball was Kiernan Dewsbury-Hall, so he’s my man of the match. His passing has been excellent, and when he’s not been on the ball he’s hustled really well.”
Where does it leave us?
Leicester climb to third in Premier League 2 Division 1 with 22 points after 12 matches - just one below leaders Chelsea, who have a game in hand.
Coming up...
The Foxes travel to Lancashire on Friday night for a Premier League 2 Division 1 clash with Blackburn Rovers at Ewood Park (7pm kick-off).
Supporters can tune into live LCFC TV coverage - completely free - from 6:45pm on Friday with former Foxes defender Sean St Ledger joining commentator Nick Walsh.
All times GMT.