Following a tight opening 45 minutes, the young Foxes went ahead as Dempsey Arlott-John opened the scoring, but Thomas Dickson-Peters levelled the scores five minutes later.
However, following successive defeats by West Ham United and Southampton, City battled through to regain their lead in the 71st minute as Oliver Murch played in Will Russ.
With the Canaries looking for another equaliser, Leicester's youngsters broke and got a goal of their own, as Johnson Gyamfi made it 3-1 with 13 minutes still to play.
As a result, the young Foxes climb to eighth in the U18 Premier League South standings, with 26 points from 21 outings during the 2018/19 campaign.
City's Under-18s now have just one league fixture remaining, a trip to Tottenham Hotspur Training Centre, to face Spurs on Saturday 27 April (11:30am BST kick-off).
The details...
City: Stolarczyk, Sams, Barrett, Murch, Obi, Loughlin, J. Gyamfi, Gbadebo, Arlott-John, Russ, Pennant
Subs not used: Bosworth, Yseko, Maswanhise, Fitzhugh, Marcal-Madivadua
Goals: Arlott-John 52', Russ 71', Gyamfi 77'