Paul Lenchner netted a consolation for Chigwell in the last 15 minutes.
Brady player-manager Josh Dagul told JC Sport: "The team were absolutely fantastic today. We only had 11 players available but the team showed unbelievable spirit and fight on a very tough pitch.
"We played some good stuff and our second goal in particular was a great team move. Daniel and JJ were the match-winners, but the back five with Jason Davis and Mike Beaber sitting in front of them also deserve a mention for their performances today, as well as young Nathan Harrod on the wing. We are looking forward to the quarter finals now."
Slater told JC Sport: "'We didn't start playing until the second half, giving ourselves an uphill battle. The pitch was pretty poor and it was without doubt the worst refereeing display since I've been running Chigwell Athletic. Second half wee turned the screw but it was too little too late."