Burke made sure she advanced automatically to the final after finishing 12th in semi-final A, just enough to progress with the top 12 from the two qualification groups doing so.
Wain, who is making her World Cup debut in Chengdu, couldn't quite follow suit as she placed 19th in semi-final B however she was among the next 12 highest points scorers.
That allowed her to progress to the final however the same fortune wasn't afforded to the third of the British women in action in China as Kate French missed out.
French placed 17th in semi-final A but, with scores in semi-final B higher, she didn't make the final with Britain's four-strong men's team set to compete on Thursday.
Like Wain, Tom Lees will be making his World Cup debut in China and is joined by double Olympic Nick Woodbridge as well as Joe Evans and Sam Curry.