The Clarets finally broke the deadlock through Treacy’s 74th minute cross-cum-shot from the left-wing which debutant Sam Johnstone misjudged and the ball crept in at his near post.
Burnley doubled their lead through Vokes on 79 minutes when he turned in Scott Arfield’s shot after Danny Ings’ header had hit the post.
In their first-ever league meeting, the visitors gave a debut to Manchester United loanee goalkeeper Johnstone due to Marek Stech’s hand injury.
The home side had the bulk of possession in the opening five minutes, but were unable to break down a resilient and organised Yeovil outfit.
Ross Wallace unleashed a seventh-minute effort from 35 yards that Johnstone did well to parry behind.
Two minutes later, Vokes attempted an ambitious volley from the edge of the box after shaking off Byron Webster, but his looping effort went high and wide.
But Clarets winger Junior Stanislas breathed a sigh of relief when his 16th minute attempted clearance fell straight to James Hayter, who failed to capitalise.
Vokes should have given Burnley a 19th-minute lead after latching onto Dean Marney’s through-ball but his chip over Johnstone was off-target.
Moments later, Clarets right-back Kieran Trippier delivered a curling cross for Stanislas, whose header went safely behind as the home side turned the screw.
Following a frantic opening 25 minutes, the Somerset side gradually began to work their way into the final third, but with little end product.
That was until Liam Davis missed from six yards on 36 minutes after Tom Heaton parried Kevin Dawson’s cross into his path, but the midfielder put his shot over.
In first-half stoppage time, Trippier’s right-wing cross found an unmarked Vokes, but the Welsh international’s header went way over Johnstone’s bar.
Shortly after the break, Burnley midfielders Marney and Wallace both went into referee Scott Duncan’s book moments apart.
Edward Upson tried his luck from distance on 51 minutes but his effort through a crowd of bodies went wide of Heaton’s goal.
Ex-West Ham man Stanislas found himself on the edge of the box in a Burnley counter-attack but his 56th-minute curling effort went just wide.
And it was Stanislas again who fired in another effort for Sean Dyche’s men, but his tame shot on the hour trickled off-target.
Treacy broke the deadlock with a fortunate effort with 16 minutes to go and Burnley could have doubled their lead a minute later when Arfield went through on goal but placed his shot wide across the face of goal.
Vokes made the points safe and then a succession of saves from Johnstone late-on kept Burnley at bay, tipping David Jones’ free-kick over and then parrying Vokes’ later header to safety.