The second-seeded Indo-Swiss combination squandered a one-set lead to go down 6-3, 2-6, 6-10 to the Russian pair of Ekaterina Makarova and Elena Vesnina.
Mirza-Hingis won the season-ending championships in 2015 but were edged out by the Russian duo in one hour and 30 minutes. The defending champions had split up in August this year, but reunited for one last time in an attempt to defend their title.
This win was Makarova and Vesnina's first triumph over the Indo-Swiss pair in five attempts. The second seeds created multiple opportunities to break their opponents but could only capatalise on four of the 15 break points they had. On the other hand, the Russians came back strongly after a poor opening set, and converted five out of the six break points that they set up in the match.
The fourth-seeded Russians will meet third seeds Lucie Safarova of Czech Republic and American Bethanie Mattek-Sands in the final on Sunday.
Safarova and Mattek-Sands defeated top seeds Caroline Garcia and Kristina Mladenovic 6-3, 7-5 in the other semi-final on Saturday. 'Team Bucie', as they are fondly called, are heading into the final on a 17-match winning streak, which started at the US Open.
As a result of Mirza's loss, Mattek-Sands now has a chance of replacing the Indian as the women's doubles world number one. If the Czech-American pair emerge victorious in the final on Sunday, the 2016 WTA year-end No 1 ranking will go to Mattek-Sands.