A dominant performance saw Simon Weaver's side move to the top of the group table and provide an immediate response to Saturday's defeat to Bolton.
Weaver took the opportunity to utilise his squad to the full, with only James Belshaw and Dan Jones being, and he was rewarded with a string of impressive performances.
Tonight's opponents had come into the game having defeated Hull 2-1 in their opening fixture but Town were immediately at them with Kiernan going close in opening minutes.
Despite the number of changes there was no sign of a disjointed Town performance and Lloyd Kerry tested Stloarczyk in the visitors goal from distance soon after.
Town then had a strong claim for a penalty waved away after a handball in the box but would not be denied. With Kiernan and Stead linking well in attack, a neat interchange between the pair set up Stead to hit home from the edge of the box for his first goal of the season.
Immediately from the restart Town were right back at the visitors with Kevin Lokko heading against the post before seeing his spectacular overhead kick palmed to safety.
From the resulting corner though Town extended their lead. With Tom Walker's delivery causing confusion in the box a loose ball fell to Jones's feet and the loanee made no mistake from close range.
With Town now rampant Jack Emmett flashed a cross just out of reach of the enrushing attack and Kiernan forced Stolarcyzk into yet another save as Town looked to put the game beyond reach.
A rare lapse at the back presented an opportunity for the visitors on the half four but Shade was thwarted by the advancing Belshaw who averted the danger.
There was no let up from Town after the break as they opened the half with a marauding Jack Emmett run but Stolarczyk was equal to Stead's shot.
Having failed to make any early inroads the visitors made their final substitutions just 10 minutes into the second half as McAteer and Nelson replaced Reghba and Goosmark-Ford.
There was no time for any impact to be made though before Town went further ahead. Walker smartly cut in from the right-hand side and his shot could only be parried into the path of Kiernan who made no mistake with his finish.
The visitors rarely threatened Belshaw in the Town goal, but Shade, the pick off the Leicester side, almost pulled a goal back on 70 minutes before substitute Suengchitthawon coolly finished in the latter stages for a consolation goal.
With Grimsby and Hull unable to play their group fixture Town seized their chance and look well-placed for qualification needing only a point in their final game at home to Hull to assure qualification to the knock-out stages.
Town: Belshaw, Burrell, Lawler, Lokko, Jones, Emmett, Kirby, Kerry, Walker (Miller, 79), Kiernan, Stead (Martin, 87)
Subs not used: Cracknell, Fallowfield, Falkingham, Beck, Hall.
Goals: Stead (17), Jones (20), Kiernan (58).
Leicester City under-21's: Stolarcyk, Goosmark-Ford (Nelson, 55), O'Connor, Hughes, Flynn, Daley-Campbell, Leshabela, Wright, Shade, Russ (Suengchitthawon, 43), Reghba (McAteer, 55).
Subs not used: Pennant, Doherty.
Goals: Suengchitthawon (84).
Referee: Andy Haines.
Report by Danny Pugsley.