Strikes from Amani Richards and Trey Nyoni came either side of a Reece Evans brace at LCFC Training Ground to seal a first win in four league outings for the side coached by Adam Barradell.
After just 14 minutes, Richards latched onto Toby Ononaye's pass to beat Henry Cullen in the Norwich net, before Evans combined with Ali Mirsad and then Richards to make it 3-0 ahead of the break.
Nyoni's effort three minutes into the second half increased City's advantage, which was dented by two late strikes from Kenneth Aboh.
It's a crucial result which puts the young Foxes above Aston Villa at the bottom with 10 points to nine, also having three games in hand on their Midlands rivals.
Fulham away at Motspur Park is next up for the Club's youngsters on Saturday 11 February (12pm GMT kick-off).
The details...
City: Weeks; Lindsay, McAlinney, Joseph, Grist (c); Nyoni, Richards, Lewis, Ononaye (Neale 66'), Mirsad (T. Thomas 78'), Evans (King 69').
Subs not used: Addai, Cook.
Goals: Richards 14', Evans 37', 45+3', Nyoni 48'.