Burnley and Yeovil had never met in a competitive fixture before. The Glovers only entered the Football League 10 years ago and had never played in the second tier until this season.
He was forced into a save seven minutes into his debut from Ross Wallace's 35-yard drive. Burnley dominated and Vokes fired off target with a volley from the edge of the area.
Wales striker Vokes then wasted a better chance when he received Dean Marney's through-ball but failed to get his chip on target.
Yeovil had an opportunity when summer signing Liam Davis missed from six yards. After the break, Glovers midfielder Ed Upson had an effort from distance but it went wide.
But Burnley took control again with Junior Stanislas curling just wide and then missing the target with another effort.
And they scored twice in the final 16 minutes with Treacy's fortunate effort and Vokes's close-range goal.
It could have been worse for Yeovil, in their first season in the second tier, had Johnstone not kept out David Jones's free-kick and Vokes's header.
Burnley boss Sean Dyche:
"Our aim is to constantly sustain wins and the lads deserve it. They have been tremendous in pre-season and they have carried that into the season.
"I'm loving that Sam is claiming everything as that is what you want your goalscorers to do and should have.
"That hunger is growing in him and is disappointed that he has had one cleared off the line. He's toughening the way he plays and is in really good shape."
Yeovil boss Gary Johnson:
"We feel as though we let that one slip out of our hands. We had a good hour and we looked Championship for the first 45 minutes.
"At this level, you have to take your chances - if you don't, all opposition teams will have some part of the play and when Burnley did, we suddenly capitulated.
"We've got some people who have not hit Championship form. We haven't come in this league to be the whipping boys, so we're actually a bit disappointed by the start. We've got to be careful of a pattern where we become shrinking violets in the last 25 minutes."
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