Young goalkeeper Joel Carlowe made his debut for Fortune in a match played on a heavy pitch at Roger Bannister Sports Centre.
The swirling wind made conditions difficult but it was the Pirates who adjusted the better.
Gab Stone scored Fortune's goal whilst Steven Black missed a penalty.
Delighted Pirates boss Elliot Cukier told JC Sport: "It has been a tough few weeks for the Straw Hats. Results haven't gone our way and after dominating a poor Hertswood Vale last week, but letting the three chances they had all game go in, we knew we had a point to prove today.
"With a new striker, and a right-midfielder and goakeeper playing their second game for the Straw Hats, and their first grass games in many years, we knew we had to stick to our game-plan and make sure we focused on seeing out the result that we knew we could get.
"And for the first time in 2018, we actually managed to do that. We have some great players in our squad and today some of them really shone.
"We played some great football and got the result we wanted and we deserved.
"However we know we can do better. We have proven it throughout this season, that when switched on, we can take the fight to any team, and we look forward to our first game against Real Hendon next week and then a nice break before our final push to finish the season in the best possible way. UTSH!"