Goals from attackers Olufela Olomola and Otis Khan gave the Glovers a comfortable half-time lead, but two strikes in the second period looked to have salvaged a point for the hosts.
The Green and Whites had other ideas and captain James Bailey nodded home in injury time to secure Yeovil’s first three points on the road since March.
“Talk about never, ever giving up! That’s the story of this football club,” Way told iFollow Glovers.
“To do it with a group of players that are new and to come away with three points in the manner we have, with the subs making an impact was a great feeling. It shows great mentality which is good to have.
“The dressing room could have been feeling very different so t’s important to enjoy the moment. Fair play to the supporters who travelled.
He added: “Our club is still alive. Everyone is working together and it’s about how strong-minded you are, how determined you wake up every morning to continue the quest to win football matches.
“I love every minute of this job.”
Town head into the weekend on a high and welcome Colchester United to Huish Park.
A positive result would see Way’s side match the club’s best home start since becoming an EFL outfit, an achievement he wants the squad to eclipse.
He said: “Now we look to Saturday where if we pick up a good result it’ll be our best home start for some time so I want to look forward to that.
“I want the lads to be able to accept the challenge of that. Every time we seem to get there and feel like we have a bit of momentum, we just slip up.
“I need to make sure everything we do from now to Saturday is spot on.