Sixth-seeded Rushmi, who was stretched to three sets in all her three previous rounds, rallied from a set down to beat Australian Renee Binnie, 6-7(3), 6-3, 6-3 in a two-hour-44 minute battle.
The 31-year-old former national champion later in the afternoon entered the doubles final in the company of China's Chun-yan He, beating Treta Bhattacharyya and Shivika Burman, 6-2, 6-4.
In the singles, Rushmi struggled to find her rhythm in the first set and yet she tried to go for some ambitious shots. The stream of errors resulted in her dropping the serve in the sixth game, but she broke back in the tenth when the Australian hit a forehand long.
The set went to the tie-breaker and Binnie, 0-3 down, came back to reel off seven points to go a set up.
Rushmi was broken by a confident Binnie in the opening game of the second set but she broke back in the fourth. She then broke a cramping Binnie in the eighth game before serving the set out.
The two players looked visibly tired in the decider and Rushmi just about managed to hold out while the Australian could not last. After trading breaks early in the set, Rushmi effected the decisive break in the seventh game and Binnie called for a medical time-out. As Binnie dropped her serve again in the ninth, it was all over for her.
"She (Binnie) played a bit different today and it took me sometime to read her game. It was a lot more windy than yesterday and with the balls being lighter, I committed a few unforced errors.
"I had my chances in the first set but I was feeling a bit tired in the beginning and I had problems with shot-making. I am happy to have pulled it off," said Rushmi, who next plays-fifth seeded Keren Shlomo of Israel.
Shlomo, who is hitting with former India player Manisha Malhotra here, beat Korean Soon-mi Seo 6-1, 6-1.
Rushmi is 2-0 head-to-head against Shlomo, whom she had beaten 6-1, 6-2 in the Nonthaburi ITF tournament last year.
In another quarter-final, the other Indian Parija Maloo went down 3-6, 4-6 to Chinese Ying-ying Duan, who Wednesday had outplayed top seed Ankita Bhambri of India.
Duan now plays compatriot Yi Zhong who upset seventh-seeded Korean Yoon-young Jeong 5-7, 6-3, 6-3 in about three hours.
