A brace from Danny Hylton and a stunning strike from Peter Vincenti saw off the hosts, who slumped to their third defeat in as many games.
"We're in the hat and that's the most important thing. For the club the money is so important," said Holdsworth. "It's a great statement for the team, to come here and do that. It's a big club, we came here as underdogs and looking at the league table you can say we shouldn't have been in the game. But we've got a lot of a ability and a lot of character.
"I want to win every game I go into and it means the world to me when we do. We've definitely turned the right corner. There's a lot of belief there and the lads are getting better."
The game was a difficult one for Vincenti, whose 35-yard effort on the stroke of half time was the highlight of a battling Shots performance. He was a good friend of former footballer Mitchell Cole who died on Friday - Holdsworth dedicating the win to his memory.
"Peter Vincenti's goal, well it's about time he scored one. I doubt he'll score a better one this season," said Holdsworth. "I've got to say, Peter's friend, Mitchell Cole died yesterday. Peter and a few of the boys were really distraught earlier on and last night.
"I want to dedicate it on behalf of Peter and the club to him. Peter at lunch time was really upset. We want to dedicate the win to him and his family."
Fleetwood took the lead after 11 minutes, Junior Brown stabbing the ball home at the back post from an Alan Goodall free-kick. And the home side set up a grandstand finish when David Ball tapped home Steven Gillespie's deflected shot with three minutes remaining.
Alex Mellon almost grabbed an equaliser deep into injury time but could not quite get a toe on Dean Howell's cross.
Holdsworth admitted it was a tense finish, adding: "We made it close in the end with a mistake. While it's like that you've got to defend and I thought we were resolute and stuck by it. We were magnificent. The players were fantastic, they worked their socks off."