An action-packed first half returned no goals, as both Arsenal's Bernd Leno and Leicester's Danny Ward stood tall in their respective nets to send the teams into the dressing room at 0-0 after 45 minutes.
Leicester pushed for the equaliser and should have been back on level terms just past 80 minutes, only for Ayoze Perez to spurn a golden opportunity when it would have been easier to score.
Eddie Nketiah then bundled the ball home from close range shortly before full-time to secure the win for Arsenal.
Arsenal playmaker Mesut Ozil was a notable omission from Mikel Arteta's side.
When asked about the German's absence, the Spaniard replied: "The team is evolving, you can see the level they are achieving.
"This is where we are at the moment. We want to evolve more and play better and compete better. We need to keep maintaining that.
"I'm really happy with the performance here, how difficult they're making things for the coaching staff to select the squad."
Leicester boss Brendan Rodgers revealed after the game that Wilfred Ndidi picked up a groin injury in his team's 4-2 win over Burnley on Sunday and could be out for up to 12 weeks.
"We are just waiting to hear more on that, but he could be anything between six and 12 weeks,'' Rodgers said about Ndidi.
"It is an abductor injury -- it may have come off the bone, which could be a nasty injury. So we will wait to see if needs an operation. If it does, then it will be 12 weeks.''