Nathan Smith bundled home an opener just past the hour before centre-back partner Alex Lacey doubled the Glovers’ advantage two minutes later.
Plymouth pulled one back through former Town defender Jakub Sokolik, but Yeovil held firm to record their first league win of 2017.
“I’m pleased for the players – they deserved it,” Way told YTFC’s official YouTube channel.
“I’ve been saying every week they’ve deserved a little bit more and we have been close in a number of games now.
“The effort, energy and desire from the players was fantastic and I thought our strength was our passion.”
He added: “I thought the players did well playing on that pitch because it was difficult to run on let alone shift the ball from left to right.
“It’s nice to have a group of players that keeping driving every minute of every day and you could see that in their performance.
“It was a big game and it was nice to get three points.”
Both Smith and Lacey’s goals came from set-pieces – an inch-perfect corner from Ben Whitfield and a low free kick from Matty Dolan.
Way was happy to see the defensive duo get on the scoresheet and praised assistant manager Terry Skiverton for his hard work on the training ground.
“They’ve been working hard,” he said.
“They’ve been working hard with Terry and he’s taken great ownership of the set-plays.
“A lot of credit goes to him and I have to thank him for the hard work he’s putting in, especially in January because you need support.
“All the staff have been very supportive and at a club like Yeovil you need everyone working together.
“I don’t think there’s a member of staff who arrives in this building that doesn’t work hard for the football club.”