In a match of few chances, Vydra swept in from close range after being picked out by Wout Weghorst’s low cross.
Wolves had earlier forced saves from Nick Pope either side of half-time but mustered little in way of a response.
Burnley have now won seven points from three games since sacking Sean Dyche.
Beating Wolves moved the Clarets out of the relegation zone and above Everton, although the Toffees could leapfrog them if they beat Liverpool in the Merseyside derby later on Sunday.
Wolves remain eighth as they aim for European qualification but missed the chance to close the gap on seventh-placed West Ham.