Allrounder Connolly has come in to replace injured opener Matt Short (quad), while spinner Tanveer Sangha has been selected ahead of paceman Spencer Johnson.
Australia won the toss and elected to bat.
The pitch for Saturday's match hasn't been used yet this tournament, and it looked dry and cracked.
The spin of Connolly and Sangha could prove crucial to complement frontline spinner Adam Zampa and part-timer Glenn Maxwell, with India again selecting four spinners.
"It looks a lot drier (than the pitches we've used). It should take more turn," Australia captain Steve Smith told Prime.
"It's the reason for batting first. We'd like to get runs on the board.
"They're a very good side India, and we like coming up against them."
Australia had the option of selecting Jake Fraser-McGurk or Aaron Hardie to replace Short, but the all-round talents of Connolly earned him the nod.
Connolly, 21, and 23-year-old Sangha have played just three ODIs apiece.
Australia started their campaign with a thrilling five-wicket win over England, chasing down an ICC-tournament record victory target of 352.
Their next match against South Africa was washed out without a ball being bowled.
Then against Afghanistan, Australia were flying at 1-109 after 12.5 overs chasing 274 for victory before rain washed out the rest of the match.
India were undefeated in their group stage, beating Bangladesh, Pakistan and New Zealand along the way.
The blockbuster clash between Australia and India is a re-match of the 2023 ODI final, won by Australia.
The winner of the semi-final will take on either South Africa or New Zealand in Sunday's final.
AUSTRALIA: Travis Head, Cooper Connolly, Steve Smith (capt), Marnus Labuschagne, Josh Inglis, Alex Carey, Glenn Maxwell, Ben Dwarshuis, Nathan Ellis, Tanveer Sangha, Adam Zampa.
INDIA: Rohit Sharma (capt), Shubman Gill, Virat Kohli, Shreyas Iyer, Axar Patel, KL Rahul, Hardik Pandya, Ravindra Jadeja, Kuldeep Yadav, Mohammed Shami, Varun Chakravarthy.
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