With the score level at 2-2 in injury time, the game looked to be headed for penalties but experienced frontman Francois Zoko came off the bench to fire the Glovers into the final four for the first time in their history.
Fleetwood were the fifth Sky Bet League One outfit Way’s side have seen off this season and the Green and Whites will need to overcome another in Shrewsbury Town to set up a tie against Lincoln City at Wembley.
It’s a task the Yeovil boss is relishing and one his squad fully deserve in his eyes.
“It’s an amazing achievement. We in the dressing room believe we can achieve something this year,” he told iFollow Glovers.
“The players deserve this. If you look at our pathway to play Manchester United (in the Emirates FA Cup), it wasn’t easy. If you look at our pathway to get to the semi-finals… that is an unbelievable achievement.
“We’ve beaten Plymouth and Wimbledon who came with strong teams and now we’ve beaten Fleetwood who have signed two players in Paddy Madden and (Toumani) Diagouraga who are way out of our league.
“It’s a fantastic moment for the football club. You could see they brought on their best players; they came down with a strong team and didn’t take things lightly.
“I’m very pleased for the players and the supporters. To get the result was deserved.”
Way praised several of his players post-match; goalscorer Corey Whelan, Jared Bird, Alex Fisher and Rhys Browne all receiving a mention but the 38-year-old reserved special comment for Zoko.
The Ivorian was introduced to the action midway through the second half and took the match by the scruff of the neck to settle its outcome.
“Francois has a huge responsibility to show leadership at this football club,” Way said.
“I’ve been doing a lot of work with him off the pitch with regards to his football development and education because I feel that’s important.
“Before he went on the pitch I asked him to lead the players to Wembley and he couldn’t have done that any better.”