World number 37 Barty snatched an early break in the second game before consolidating in the sixth to claim the opening set.
Latvian Ostapenko failed to offer any kind of resistance in the second set as Barty reached her first Premier 5 tournament final.
The 21-year-old Barty has claimed three wins over top-10 ranked players this week, including a scintillating comeback against world number four Karolina Pliskova in the quarter-finals.
"It doesn't matter whether it's the first round at Wimbledon or the final here tomorrow. I think for me I try and approach the match the exact same way," Barty said.
Barty is bidding for her second title of the season after winning in Kuala Lumpur in March.
Her opponent in Saturday's final is France's Caroline Garcia, who beat Greek qualifier Maria Sakkari 6-3 6-2 in the other semi.
Garcia advanced past the semi-final stage for the first time in five attempts this year and will also play in the first Premier 5 level tournament final of her career.
"It feels good, it was a long time without a final," Garcia said.
"It was such a fight today, and she (Sakkari) had a great week coming from qualies and I’m very happy with the way I played."
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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