In Sharma's case that included launching Kane Richardson out of the ground.
Sharma smashed four sixes and six fours in his 71 before being caught in the deep off the bowling of Nathan Coulter-Nile (1-58), while Rahane was trapped in front by Pat Cummins (2-54) for 70.
Australia got the wickets of Virat Kohli (28) and Kedar Jadhav (two) in quick succession to put the hosts at 4-206.
Hope was all but extinguished a short time later when Steve Smith dropped a touch chance to dismiss Hardik Pandya on 42.
He went on to make 78 off 72 balls before Cummins had him caught at mid-on with 10 runs to get.
Earlier, Aaron Finch returned from a calf injury in style by smashing 124 off 125 balls, but again Australia's middle order crumbled when they were most needed.
Opener David Warner made a handy 42, while No. 3 Smith was furious with himself when he got out caught at long-off for 63.
When Finch departed after a slog sweep went down deep mid-wicket's throat, the rot set in.
Australia lost 5-51 in a 10-over period and could only muster three boundaries in the final 11 overs of the innings as the Indian attack tightened the screws.
Glenn Maxwell (five) and Travis Head (four) both failed, while part-time wicketkeeper Peter Handscomb made three and dropped Sharma on 67 after being brought into the side following Matthew Wade's axing.
Left-arm spinner Ashton Agar dislocated a finger on his right hand while fielding but returned to bowl to complete his 10 overs, finishing with 1-71.
