Raúl Uche Rubio's early header put the Foxes in front before Okera Simmonds' equaliser after the break, but a Bartosz Kapustka strike and Layton Ndukwu's late brace sealed all three points.
City’s youngsters, whose line-up included six changes and a maiden outing for Çağlar Söyüncü in defence, started brightly with Uche Rubio hitting the base of the post after 10 minutes.
In the build-up, it fell to Ryan Loft on the right flank and the former Tottenham Hotspur man located Uche Rubio at the far post, but the Spaniard’s effort came back off the woodwork.
Uche Rubio only had to wait until the 19th minute for his goal, however, as he latched on magnificently to Kapustka’s free-kick, from the left flank, before glancing it into the net.
His celebration, meanwhile, was also a spectacle to behold as the 20-year-old launched himself into a backflip before accepting the congratulations of Hamza Choudhury.
Loft and Ndukwu tested Andy Fisher before the break but the Foxes found themselves level just after half-time as a deflected effort from Simmonds evaded Viktor Johansson in the net.
However, parity on the scoresheet lasted just two minutes with Kapustka pouncing to restore City’s advantage, benefitting from Uche Rubio’s searching cross to tap it in at the far post.
Minutes later, Ndukwu, in fine form for Leicester, went desperately close to adding to his side’s goals tally with an audacious effort from distance, which whistled inches wide of the visitors' goal.
The 19-year-old tried his luck once again on the hour-mark, attempting a chip over Fisher in the Rovers net from outside the penalty area, but it came back off the crossbar.
He rattled the woodwork yet again shortly after from the angle of the 18-yard box, before finally notching on the scoresheet with a hopeful shot which deflected in.
It got better for City's skilful winger, adding another in added time after good work by substitute Calvin Ughelumba, as the hosts wrapped up a hugely satisfying evening in Whetstone.
Major moment…
Less than 120 seconds after losing their one-goal lead, up stepped Bartosz Kapustka to regain it, ghosting into the box to finish Raúl Uche Rubio's cross.
It was a moment in which the game hinged and set the Foxes on a path towards their second victory of the season in front of Leicester City manager Claude Puel.
Who impressed?
The contribution of Raúl Uche Rubio was a significant influence over the eventual result in Whetstone with the Spaniard having a key role in both goals.
A special mention must also go to Layton Ndukwu who struck the woodwork on two separate occasions - but his efforts yielded their due return with two goals later on.
Where does it leave us?
Leicester’s reward for this victory is a climb up to second in Premier League 2 Division 1 on six points, one behind early pace-setters Manchester City.
Coming up…
City’s youngsters head to Pride Park to tackle Derby County on Monday 3 September in Premier League 2 (7pm BST kick-off) – a fixture you can watch live on LCFC TV.
The details…
City: Johansson, Ramsay, Elder, Choudhury (c) (Ughelumba 81), Pascanu, Söyüncü, Kapustka, Kaba Sherif (Dewsbury-Hall 54), Loft, Ndukwu, Uche Rubio (Shade 72)
Subs not used: Davies, Tee
Goals: Uche Rubio 19, Kapustka 50, Ndukwu 79, 90+4