Jadhav (81) and Dhoni (59) ensured India chased down the target of 237 with 10 balls to spare and took a 1-0 lead in the five-match series.
India got off to a bad start in the second innings as Shikhar Dhawan was dismissed for a duck in the beginning of the second over itself, giving a simple catch to Glenn Maxwell at point.
This brought out Virat Kohli, who proceeded to put together a 76-run partnership with Rohit Sharma that begun on a circumspect note but once the two were settled, runs flowed at a consistent pace.
Kohli, in particular, looked ominous but was trapped in front of the stumps by Adam Zampa, whose decision to go for the review paid off.
Kohli’s dismissal led to a bit of a wobble. Rohit departed soon after, giving a simple catch to Aaron Finch before Ambati Rayudu edged one to Alex Carey behind the stumps.
With 138 still to win, the onus was now on MS Dhoni and Kedhar Jadhav to build a partnership and get India home.
The two were patient for the most part, rotating strike whenever possible and not looking to play any risky shots and their approach was eventually rewarded as they brought up a 50-run stand.
The propensity for taking risks increased slightly thereafter as both Jadhav and Dhoni looked for boundaries so as to ensure the run-rate stayed in control.
Jadhav would eventually go on to bring up his 5th ODI fifty and then continued to take on the bowlers with some success. Dhoni would eventually bring up his 71st half-century in the format in the 48th over.
Jadhav ended the over with a six and Dhoni finished the chase in the first two balls of the 49th over after scoring two boundaries.
Earlier after the hosts were asked to bowl, Mohammed Shami put in an inspired spell that saw Australia restricted to just 236/7.
Shami returned impressive figures of 2-44 including the wicket of in-form Glenn Maxwell for 40 while Kuldeep Yadav (2-46) and Jasprit Bumrah (2-60) also played their part.
Alex Carey made an unbeaten 36 while Nathan Coulter-Nile (28) put together 62 runs for the seventh wicket to give the Aussie total some respectability after the looked like they would struggle to cross even the 200-run mark.
Australia were rocked early by the hosts when skipper Aaron Finch – who was playing his 100th ODI – departed without troubling the scoreboard after he was caught behind off Bumrah in the second over.
Usman Khawaja, who top-scored for the visitors with 50, put together an 87-run stand with Marcus Stoinis to steady the innings against a bowling attack that looked hungry for wickets.
Kedar Jadhav, who has a knack for taking key wickets in the middle overs, got rid of Stoinis for 37. Kuldeep then came to the party.
First, he sent Khawaja back to the pavilion soon after the left-handed opener had completed his sixth ODI fifty and then he got Peter Handscomb stumped for 19 to put Australia on the back foot.
Maxwell threatened to disrupt the hosts' plans but skipper Virat Kohli's move to bring back pace spearhead Shami in the 36th over paid off and the hard-hitting batsman was bowled on 40.
Shami soon got rid of debutant Ashton Turner as well and despite a late flourish from Coulter-Nile and Carey, Australia could not set India a big total.
The second ODI takes place at Nagpur on Tuesday (March 5).
Aaron Finchadam zampaAlex Careyambati rayuduashton turnerGlenn MaxwellIndia vs Australia 2019jasprit bumrahKedhar JadhavKuldeep Yadavmohammed shamiMS DhoniNathan Coulter-Nilepeter handscombrohit sharmashikhar dhawanUsman Khawajavirat kohli
First Published: March 2, 2019, 9:42 PM IST