Gamildien scored first from a superb free-kick and then caught Buccaneers goalkeeper Richard Ofori well off his line from 35 yards out.
Kabelo Dlamini pulled a goal back for the Sea Robbers from the penalty spot but it was not enough as the holders crashed out.
"The Glory has to go the team," Gamildien told SuperSport TV.
"We worked very hard. We have a new squad. The coach always told us believe in yourself, go out there and be fearless. I'm glad we could pull off this big upset and onto the next one.
"I've been practising in training and I knew I was going to get one this game. I just had to get it on target and I knew it was going to go in.
"I saw the keeper out of his area and I just had to make sure that I got it on target and it went in.
"The pressing is part of our DNA. The coach emphasises that we must press responsibly and keep teams under pressure. Like you saw today it worked out in our favour."