Sam Surridge was on target twice, either side of Olufela Olomola’s 27th-minute strike, as the Glovers comfortably defeated their Sky Bet League Two counterparts.
Despite being down to nine men after Olomola and Francois Zoko received red cards, Yeovil remained on the attack for a fourth goal and were solid defensively to hold on to an impressive clean sheet.
“I’m very pleased,” Way said.
“Stevenage are a very good team and very effective but we didn’t let them have anything today and it could’ve been six in the first half.
“The players put the tactical plan into practice unbelievably well with tempo at the start of the game. The way they finished the goals off was a credit to them.
“The players have to take credit for the way we exploited their weaknesses and it was very pleasing as a manager to watch that.
“The discipline to keep a structured, organised, competitive defensive unit with less players is not easy so that was very good.
“We were in control from start to finish. In the end we were playing with two less players and still getting in. The confidence in the group is growing.”
Way believes Town’s fine display was highlighted by the home support who were in good voice all afternoon.
He said: “The supporters deserve huge credit.
“They were singing the players’ names and there were songs of ‘we love Yeovil’ and you have to put in a good performance for them to sing that. A big thanks to them.”