Pandya struck a career-best 83 and Mahendra Singh Dhoni made 79 to help the hosts overcome a top-order collapse and post 281-7 at the MA Chidambaram Stadium.
However, a lengthy mid-innings rain break left Australia needing 164 runs in 21 overs to go 1-0 up in the five-match series.
Glenn Maxwell smashed 39 and James Faulkner made 32 not out but Pandya (2-28) and India's spin duo of Yuzvendra Chahal (3-30) and Kuldeep Yadav (2-33) combined to restrict Australia to 137-9.
Earlier, home captain Virat Kohli's decision to bat appeared to backfire when Nathan Coulter-Nile's three-wicket burst reduced India to 11-3 inside six overs.
Kedar Jadhav and Rohit Sharma then added 53 runs for the fourth wicket to arrest the slide.
Jadhav lived dangerously to score his 40, while Sharma made 28 before both fell to Marcus Stoinis, leaving India reeling at 87-7 in the 22nd over.
A 200-plus score looked a distant dream for the hosts at that stage but Pandya and Dhoni had other ideas.
Pandya clobbered Adam Zampa for three successive sixes in a 24-run over, bringing up his fifty off 48 balls in the process.
The all-rounder blasted five sixes and as many fours in his 66-ball blitz before falling to the leg-spinner.
Dhoni, who took 67 balls to score his first boundary, accelerated towards the end and raised 72 runs with Bhuvneshwar Kumar who scored 32 not out.
Australia wobbled early in their chase as Jasprit Bumrah bowled Hilton Cartwright and then took a swirling skyer to dismiss rival skipper Steve Smith.
Yadav dismissed David Warner for 25 but Maxwell looked in murderous mood as he clobbered the left-arm wristspinner for three successive sixes.
Chahal ended Maxwell's 18-ball blitz and went on to claim two more wickets as India triumphed despite dropping three catches which could have cost them dearly in such a small chase.
Eden Gardens in Kolkata will host the second one-dayer on Thursday.
(Reporting by Amlan Chakraborty in New Delhi; Editing by Clare Fallon)
Share
