After David Warner fell to a spectacular one-handed catch from Manish Pandey at point on 15 and Aaron Finch was controversially stumped for 33, Smith steadied the ship.
He drove nicely down the ground and regularly swept in front of the wicket with great power, while still working the ball nicely off his legs.
The 30-year-old looked poised for his first white-ball century for Australia since January 2017, before he played on to Kuldeep Yadav (2-65) from his 102nd ball.
Smith had shared a 96-run stand with Marnus Labuschagne, who impressed in his first ODI innings with 46 from 47 balls and looked generally busy at the crease.
Together the pair looked capable of taking Australia home, as they went at close to a run a ball and had the required rate under control.
But when Labuschagne chipped Ravindra Jadeja (2-58) to long off in the 31st over, the rot began.
Alex Carey came and went for 18 when he hit Kuldeep to cover and Smith was bowled three balls later, the 120 from 73 was always going too tough of a task for Australia’s lower order.
“We timed our chase pretty well when we lose three wickets in between 30 and 40 overs, it halts the ability to be able to go and try and get ten an over,” Smith said.
“It’s pretty difficult. We lost it in that 30-to-40-over mark.”
The loss was Australia’s first of the summer, after previously winning five T20s and five Tests at home as well as the previous ODI in Mumbai by 10 wickets.
But it wasn’t all good news for India, with Rohit Sharma suffering a right shoulder injury in the field that could leave him in doubt for Sunday’s decider.
Earlier, Australia’s bowlers endured a tough time on the batter’s paradise as Mitchell Starc had for the second-worst return of his career with 0-78.
Kane Richardson also finished with 2-73 and Ashton Agar 0-63 from eight overs as Indian opener Shikhar Dhawan hit 96 and KL Rahul 80 in the run-scoring spree.
Pat Cummins bowled well for his 0-53, but Zampa was by far the tourists’ best.
He further enhanced his record against Virat Kohli, removing him for the seventh time in internationals on 78 when Ashton Agar and Starc combined to catch him on the boundary.