Daniel Selwyn had given Oakwood a first-half advantage, sending a fantastic left-footed strike from long range past RJC keeper Dan Lee.
RJC increased the pressure in the second half, with Darryl Green rattling the crossbar with a clever effort.
Hahn equalised after 70 minutes with close-range tap-in.
With the bit between their teeth, RJC went in search of the winner and it arrived on 80 minutes when some tidy build-up play resulted in a lay-off from Harrison Midda on the edge of the penalty area and skipper Aviram side-footed the ball into the top corner.
Joint-manager Aviram told JC Sport: "It was a true show of character from the boys led them to our third win in three games. Could this be the start of a magnificent winning run?
RJC right-back Martin Sales commented: "It was really was a game of two halves. We took a while to get going but once we do we can mix it with the best. I’m proud of the boys.
"We showed a lot of experience out there today and managed the game well. We are full of confidence now look like at different team to the start of the season. I was the best player on the pitch, just look at video!”
Oaks boss Jason Stein told JC Sport: "We're gutted to have lost this one. Utterly bereft at how we let that game go. We had so many chances to win it and our lack of cutting edge cost us.
“Maybe a dozen clear-cut one-on-ones, shooting chances, headers cleared off the line. We had enough to have won that game over and over. It’s a real sickener especially after taking the lead early on.
“Fair play to Redbridge C (nee Woodford) who held on through an excellent goalkeeping performance in my view and then they did not let their heads drop and got the two goals. And while I feel we were incredibly short-changed with a loss I’ll stay upbeat as the manner of the performance was overwhelmingly positive, especially at the back where we more or less kept Mitch Hahn - a special player - quiet enough. Onto Raiders B.”