India's bowlers pulled Australia back from a blistering start to restrict them to 160 for six wickets on Sunday with their final World Twenty20 Super 10 game serving as a knockout match to secure a place in the last four versus West Indies.
Hosts India, inaugural World T20 champions in 2007, and reigning 50-over title holders Australia have won two matches each, with their only loss against New Zealand, and the winners of the Group Two clash will meet the Caribbean side in Thursday's semi-final in Mumbai.
New Zealand face England in the other semi-final.
Australia's Aaron Finch (43) and Usman Khawaja (26) smashed the bowlers to all corners of the ground after captain Steve Smith won the toss and opted to bat on a pitch that was used for the women's game between India and West Indies earlier on Sunday.
Left-handed Khawaja's first six scoring shots were all boundaries, four of them coming against paceman Jasprit Bumrah in one over, with Australia racing past 50 before the completion of the fourth over.
Finch, Australia's captain in the format before he was replaced by Smith shortly before the tournament, then launched into India's bowling mainstay Ravichandran Ashwin, hitting the off-spinner for two consecutive sixes over long-on.
But some smart bowling from left-arm spinner Ravindra Jadeja and part-timers Yuvraj Singh and Hardik Pandya, who picked up two wickets, in the middle overs halted Australia's progress as they struggled to hit the boundaries.
Dangerman Glenn Maxwell (31) took his time at the crease but got out just as he started opening his arms.
Wicketkeeper Peter Nevill smashed Pandya for a four and a six off the last two balls of the innings as Australia, yet to win the World T20 title, took 15 runs in their final over to ensure India must score more than eight runs an over in their chase.