Strikes from Matty Dolan, Jean-Louis Akpa Akpro and Otis Khan saw the Glovers move seven points clear of the bottom two with the best goal difference out of the bottom eight sides in Sky Bet League Two.
With just three games remaining the result is likely to be enough to see the Green and Whites retain their EFL status, a win the Yeovil manager was delighted with.
Speaking to YTFC’s official YouTube channel, Way said: “What you could see there with the supporters at the end was a little sigh of relief.
“Just because three points when you look at the table now is huge.
“The players needed that, the whole club needed that and it’s a nice feeling.”
Dolan’s free-kick on his 100th appearance for the club and Akpa Akpro’s first Glovers goal put the hosts in a commanding position, before Khan’s goal on his first home appearance since a three-month spell on the sidelines completed the scoring.
Added in, young ‘keeper Jonny Maddison kept a cleansheet on his home EFL debut leaving Way pleased with aspects of the season overall.
“I’ve talked to the players all week about what they’ve achieved,” Way said. “It’s only going to be me that tells them what they’ve achieved.
“You look at certain players making their league debuts, Nathan Smith last week (250th appearance), Jonny Maddison (EFL debut) – there are so many positives to take from this season.
“Unfortunately, being in the position we have been makes it difficult to let them know that.”
Having returned to winning ways, the Town manager is now keen to tie down some of the key assets within his squad.
“I want to be in a position next year where I keep this group of players – and I’ve told them that.
“I don’t want to spend this year going through what we’ve gone through – highs and lows – because I think the experience they’ve gained will help us really kick on next year.
“Unfortunately, that sort of stuff is out of my hands.”