Catford had opened the scoring when a cross-shot drifted into the net.
Fortune showed tremendous heart and character to initially level, through Gab Saul, before edging ahead, via Jonny Pressman.
The visitors looked set for what would have been their third league victory, but they lost concentration right at the death, allowing Catford to equalise.
Fortune joint-manager Steven Black told JC Sport: "The feelings within the squad are mixed today. Whilst we are gutted to only take home a point, I am personally delighted with the continued improvement in this team.
"Every single man gave 110 per cent and we can ask no more than that. It just wasn't to be today. That said, we can go into next week's game with lots of confidence and we will demand the same again as an absolute minimum."
Reflecting on the game overall, in which Catford finished with 10 men after a red card for violent conduct, Black went on to say: "The only negative from this morning was the behaviour shown by Catford's management, towards match referee Stuart Ansher. At a time when our league should be pulling together, no referee should be giving up their Sunday morning to be subjected to aggression and abusive language. Without our referees we have no MGBSFL and every team in the league should be doing their utmost to ensure this doesn't happen."