The Blues Under-21 side maintained their unbeaten start to the season after Brown netted the opener in the first half.
The Foxes managed to level through Gary Taylor-Fletcher after the interval with a neat volley.
Chelsea posted a clip of the goal, which saw the 17-year-old curl a strike into the top right-hand corner from 20 yards out, earning Brown his first goal of the season.
Speaking to the official Chelsea website after the match, development manager Adrian Viveash said: ”It was a tough game.
”It was really great for us to play against an Under-21 team with the calibre of some of their players. Taylor-Fletcher obviously has a wealth of experience.
”Our back four were very good and we were able to stay in the game at times because of them. Izzy Brown worked his socks off up front but our technical players didn’t have their best days and that affected us.