Woodingdean substitutes, Ed Bradley and Tariq Richards, combined for the latter to go close, before captain Max Jeffery nodded wide with his header at the back post.
But with Wanderers having to chase the game, their attacks grew increasingly frantic, with the Dons content to contain and hit their opponents on the counter.
Demario almost added a second and Josh Gould could have put the result beyond any lingering doubt, but his shot was cleared from under the crossbar by a defender.
That looked to be the final action of the game, but Woodingdean were handed, quite literally, the latest of lifelines with a free-kick on the very edge of the area in the dying seconds.
Beebee’s side could have saved themselves and set up the drama of a penalty shootout, but James Waters' set piece failed to find the net, and, with that, the cup was won.
Speaking after the game, Dons manager Charlie Brown couldn’t have been prouder of the performance his team put in.
“We pride ourselves on our attacking play,” said Brown, “our pressing, our creativity and the way we try to play. But tonight, I felt our defence won us the game, we kept them at arm’s length and were so well organised.
“We all know Harley [Demario] is a player of real quality, but I also thought Luke [Burbridge] was magnificent in there for us. He went down with cramp and we had to take him off for a breather but he couldn’t sit still. He had to get back out there and for me that epitomised his performance.
Assistant Manager, Tony Woods added: “It’s fitting we’ve achieved this tonight as last year’s win was the last trophy Matt Major (the late Sussex County FA chairman) handed out and I think we showed a lot of the qualities he would have liked - hard work, teamwork, determination and desire.
“Me and many of our lads were close to Matt so we feel we’ve owed him that. We’re doing well in the league and now have this cup in the cabinet again, so we can go and enjoy this one."