The visitors impressed but second-half goals from Keith Treacy and Vokes, who has now scored two in two games, chalked up a second win of the season for Dyche's men.
And the former Watford boss is convinced that Vokes and Danny Ings, who hit the post with a header to set up his partner's goal, are a match made in heaven.
"Our aim is to constantly sustain wins and the lads deserve it," he said.
"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.
"Ings hit the post and they were quiet in the first half, but in the second half along with the rest of the team we started building.
"It's good signs but early signs so there's still a hell of a lot of work to do. There are no guarantees in the Championship.
"We knew they would give us a hard game and so I'm pleased to come out with a win."
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.
Liam Davis then missed from six yards for the Glovers in the 36th minute after Tom Heaton parried Kevin Dawson's cross into his path.
Ed Upson tried his luck from distance on 51 minutes, only for his effort through a crowd of bodies to fly wide of Heaton's goal, but Treacy broke the deadlock on 74 minutes when his cross-cum-shot from the left wing deceived Sam Johnstone.
Vokes then put the finishing touches to the win, leaving Glovers boss Gary Johnson a frustrated figure.
"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," he said.
"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.
"Our subs were not as effective as theirs on the day late on and we got gradually less effective, especially when they got their first goal.
"I was disappointed we didn't give it a right go to get back into the game. 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."