After losing 4-3 to Tottenham Hotspur at Belvoir Drive before Christmas, the young Foxes were determined not to let history repeat itself on the opening matchday of 2020.
They were ahead on 28 minutes through a nicely-taken penalty from Sidnei Tavares, although the Canaries levelled just two minutes later through Tyrese Omotoye.
However, City's youngsters regained their lead and then lost it again before the break as Kasey McAteer struck for Leicester in Norfolk before Thomas Dickson-Peters equalised.
After the interval, the match threatened to get away from the visitors as Jon Rowe and then Tony Springett made it 4-2 before the 70th-minute mark, but it merely sparked City into life.
Kian Pennant got one back for the young Foxes on 80 minutes before, with only seven minutes of normal time to play, McAteer's second of the day sealed a vital point.
The young Foxes drop one place to sixth in the U18 Premier League South standings on 15 points from 12 outings, four of which have been wins and three draws.
Next up, on Saturday, Leicester welcome Reading to Belvoir Drive (12pm kick-off) before travelling to Fulham on Saturday 18 January (12pm kick-off).
The details...
City: Bosworth (c); Godsmark-Ford (Levi Yfeko 65'), Aisthorpe, Sams, Barrett; Maswanhise (Fitzhugh 70'), McAteer, T. Pennant (Russ 88'), Loughlin; K. Pennant
Subs not used: Weeks, Flynn
Goals: Tavares pen 28', McAteer 33', 83', K. Pennant 80'
All times GMT.