- 1,612
- 9
- 38
Burrage is also enjoying the best week of her career having never previously made a WTA quarter-final, and she produced another hugely impressive performance to beat France's Alize Cornet 7-5 7-5.
It was a topsy-turvy contest featuring 10 breaks of serve but Burrage made her extra power count.
"I wasn't expecting this coming into this week," said Burrage, 24. "But I'm very, very happy with my performance today. It's going to be an amazing day tomorrow. What an amazing tournament for both of us."
Burrage would break the top 100 for the first time and overtake Boulter as British No 1 should she lift the trophy.
That would put both in a strong position to qualify for future grand slams by right, and Boulter said: "We were maybe a little bit too early to put some negative stuff out.
"It's very easy to focus on one or two tournaments but I think, bigger picture, we're in a great place and I'm happy to say that and stand by it."
In the 50 years of the WTA Tour, the only previous all-British finals saw Sue Barker and Virginia Wade split victories in Paris in 1975 and the Virginia Slims of San Francisco two years later.