Diksha Dagar, who shot 67-72 in her earlier two rounds finished 6-under 210 for the week and was four shots behind the winner, Amy Taylor of England, who closed with 69 after 70-67 on the first two days
Diksha Dagar was the best among the five Indians in the field. Vani Kapoor (72) was T-30, Pranavi Urs and Tvesa Malik with 73 each were T-41 and Ridhima Dilawari (75) was T-76
After registering a win in one hour and 28 minutes, Gauff and Routliffe will take on Italian hopes Sara Errani and Jasmine Paolini for the WTA 1000 title.
The Chilean struck 23 forehand winners to register a 3-6, 7-5, 6-4 victory, spoiling Tsitsipas' hunt for a third successive semi-final appearance in Rome.