The score remained the same until 73rd minute when three one-touch passes, starting with Fierstone to Rob Blackman who passed it to sub Sherman to score the second.
Five minutes later it was 3-0 after Weinberger happened to be in the right place to tap the ball into the net.
Redbridge scored their goal towards the end of the game through centre half Brad Frankel.
Delighted Brixton boss John Nitka told JC Sport: "As I said last week, with a few players back from injury we would be a hard team to beat.
"Do not take it away from Redbridge, they are good and a physically, strong team as they continually battered our defence, but we held out until the end.
"All the same it was a great result for us."
RJC manager Eilon Kennt told JC Sport: "I did say this would be hard and we would need to be at our best. Unfortunately, we weren't.
"By the time we started to play properly, we ran out of time.
"It's always the same when you're chasing a game, you end up with a catalogue of near misses, but well done to Brixton - they made less mistakes and scored more goals.
"Now we'll start focusing on next week's game against Hendon."