The scoring was started just five minutes in by Luqman Aideed, who sent his shot from inside the box into the top corner.
It remained 1-0 until early in the second half, when Leicester punished the Gunners on the break. Finishing off a fast break, Riley Carr set up Lorenz Hutchinson to double the advantage.
Two became three on the hour mark, via a corner, which led to Tommy Neale assisting Hugo de Lisle to strike from outside the area.
The fourth would come from Admir Bristric, again made by Carr, with the Bosnian gaining minutes for the Development Squad.
The visitors' consolation goal quickly followed, scored by Ceadach O'Neill, though it would not have any bearing on the end result.
A first PL2 victory of the campaign, it lifts the side coached by Leon McSweeney up to 23rd in the table, with four points from the opening five league games.
Turning attention to the Premier League International Cup on Friday, City host Sporting CP from Lisbon in a 7pm GMT kick-off.