Andy Robinson and in-form Lee Trundle were the heroes as the Third Division side booked their place in the last 16 at the expense of the Lancashire club.
Swans hit-man Trundle has now scored in every round of the competition and the result was all the more impressive as they were a goal down to a Dickson Etuhu header.
"What we wanted to do all week was to try and put on a cracking cup performance for the fans and we did that today, with a fairy-tale ending," Flynn said.
"I said to the players at half time that we are still in the game and we should go for it by making chances and thankfully that is what happened.
"There were a number of good saves from both keepers but it has turned out to be a day for us to remember.
"A year ago, Andy Robinson was playing Sunday League football but today he played in front of 10,000 passionate fans and gave them something special with that superb free kick.
"Preston are a good side but the response from the players after they went a goal behind was magnificent."
