The young Foxes in fact took the lead at Meadow Park, with Tom Wilson-Brown netting for the visitors.
It was an advantage that only lasted five minutes, though, as the Gunners restored parity in first-half added time via Ethan Nwaneri's finish. The dismissal of Paul Appiah for City then changed the pattern of the game in Borehamwood.
Nwaneri doubled his tally to make it 2-1 on the hour, before James Lannin-Sweet added another five minutes later. Nwaneri notched his hat-trick and a fourth for the home side in the final moments to seal the victory.
A trip to Lancashire FA County Ground to tackle Blackburn Rovers Under-21s is next up for City's youngsters on Sunday 27 August. The side coached by Ben Petty are 14th in the new-look 26-team Premier League 2 table.
The details...
City: Young; Joseph, Appiah, Wilson-Brown, Ali; Richards, Cover, Amartey (Lewis 78'), Cartwright (Evans 63'), Hill (Lindsay 46'); Pennant (Grist 50').
Subs not used: Doherty.
Goal: Wilson-Brown 42'.