The number one seeds were pushed to the limit by Spaniards Anabel Medina Garrigez and Arrantxa Parra Santonja.
After a battle that lasted nearly two hours, the Indo-Swiss pair prevailed 7-5, 6-7 and 10-6.
“The match was so long and close because we were facing very tough opponents,” said Sania after the win.
They will face Vera Dushevina and Barbora Krejcikova in the finals.
“We are to clash with an international pair who has a Russian player. But the Russian fans are fair, so we are sure we will get our share of applause” Hingis was quoted as saying by wta.formulatx.com.
Sania and Martina have now won 39 matches on the trot and are just 6 away from equaling the all-time record of 44 set by Jana Novotna and Helena Sukova in 1990.