There were a number of chances from both teams but the scoreline remained 1-1 at half-time.
Brady started second half brightly and missed a couple of chance before Brad Gayer put Fairlop ahead with a sensational trademark lob from 30 yards.
Brady didn't let their heads drop and drew level from the spot when Ollie Levy was brought down. Kohler stepped up to score his and Brady's second, calmly slotting home
A tight game was always likely to be settled by a moment of magic and it arrived when Ricky Rinder released Cohen with an exquisite pass and he calmly slotted the ball home.
Fairlop threw the kitchen sink at Brady but they held firm and secured their place in the next round.
Brady boss Joel Nathan told JC Sport: “It was great to come away from with a win. We showed from 1-12 that we can battle when need to and let our feet do the talking.
"Roll on next week when we face Hendon as we know we need to be at our best to get a result."
