Australia couldn't recover from Smith's wicket as they lost wickets at regular intervals thereafter to be bowled out for 304, as India picked up a 36-run win to level the series.
India's pacers bowled yorkers in the death as Australia's lower order faltered.
Smith scored an ODI fifty to resist India's attack, but fell on 98 - two short of what would have been a deserved century.
Aaron Finch stitched a 62-run stand with Smith before he was stumped. The decision was debated on, but Finch had to depart in what was quite a close call.
David Warner fell early in a steep chase, failing to get going in the second ODI.
KL Rahul's late assault gave India 340 with India scoring over 50 runs in the last five.
Zampa then got the wicket of Kohli at a crucial time to peg India back a tad bit.
Kohli came in at his usual No.3 position and scored another half-century, adding 78 runs with KL Rahul.
Shreyas Iyer fell soon after, as Zampa picked up his second wicket.
Dhawan fell on 96, missing out on a hundred pulling to fine leg.
Kohli came in at his usual No.3 position and added over 100 runs with Dhawan.
Rohit Sharma was trapped leg before to Zampa for 42 after an opening stand of 81 with Dhawan.