Kuznetsova, who won the Miami title in 2006, will next meet either Victoria Azarenka of Belarus or second seed Angelique Kerber of Germany who were scheduled to play their semi-final later on Thursday at Crandon Park.
"I am happy that I could hang in there and never let my hands down," Kuznetsova told ESPN in a courtside interview. "I have not been feeling my best but I have been fighting every ball and just trying to run as much as I could.
"I was praying to finish it in two sets so I can have a little bit of time to rest," smiled the Russian, referring to Saturday's final.
"I really tried to enjoy the match, even though I couldn't feel my best shots. I had to fight. This is what tennis is about."
Kuznetsova, who pulled off a stunning upset when she ousted world number one Serena Williams in the fourth round, won a hard-fought opening set after ending a brilliant baseline slugfest between the two with an overhead smash.
Though she failed to hold serve in the first game of the second set, the Russian broke her 19th-seeded opponent in the second and fourth games to lead 3-1, then fought back from 15-40 down on serve in the ninth to seal victory.
Bacsinszky, who beat third-seeded world number two Agnieszka Radwanska of Poland in the fourth round, converted just two of 14 breakpoint opportunities during the match.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)
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