Australia's batting woes continued as they once again failed to read Kuldeep Yadav's left-arm wrist spin and the Chinaman finished with figures of 2/16 in 4 overs. Meanwhile, Jasprit Bumrah (2/17) and Yuzvendra Chahal (1/23) also played their part to perfection.
With this victory, the 'Men in Blue' have now taken a 1-0 lead in the three-match series and the second match will be played in Guwahati on Tuesday.
The hosts were given a target of 48 runs to chase in 6 overs after rain played spoilsport right at the end of the Aussie innings. Rohit Sharma and Shikhar Dhawan were given the task of chasing down the score, with required-rate set at 8 per over.
Rohit continued his good form as he hit a boundary on the first ball of the innings off debutant Jason Behrendorff. Then on the first ball of the second over, Rohit hit a huge six off the bowling of Nathan Coulter-Nile and at this point the hosts were flying in the chase.
But Coulter-Nile hit back hard and castled Rohit on the next ball, right after getting hit for a six. Kohli and Dhawan then saw India home with three balls to spare. Both hit three boundaries each in their respective innings and didn't give the Aussie bowlers a chance.
Kohli even finished off in style in Dhoni's homeland, as he hit a boundary to get India over the line. Kohli and Dhawan put on an unbeaten 38-run partnership for the hosts and India won the match with no further jitters after Rohit's wicket.
Earlier, Indian bowlers starred as Australia were restricted to a meager 118/ 8 when rain stopped play after 18.4 over. David Warner was castled by Bhuvnehsvar Kumar in the first over of the innings itself after the southpaw had hit him for two boundaries.
Aaron Finch and Glenn Maxwell then steadied the ship for the hosts and then started to take the attack to the Indian bowlers. At one point, Australia were batting really well, as they crossed the 50-run mark in just 6.1 overs.
However, it all changed when, Maxwell gave a simple catch to Bumrah at short mid-wicket off the bowling of Chahal. Kuldeep then further dented the visitors by dismissing Aaron Finch (42) and Moises Henriques (8) off successive overs.
It was Finch's dismissal that brought about Australia's downfall. Finch looked in fine form with four boundaries and one six but against Yadav, he looked determined to play the sweep shot. After playing five sweep shots, Yadav bowled one fuller that breached his defence.
The wicket virtually sent alarm bells ringing in the Australians camp as Yadav and Chahal went through the middle overs restricting their flow of runs before Bumrah's twin bursts in the 18th over.
Aaron FinchBhuvneshwar KumarDavid WarnerDuckworth and Lewis Systemind vs aus 2017India vs Australia 2017jasprit bumrahJSCA StadiumKuldeep Yadavvirat kohli
First Published: October 8, 2017, 7:46 AM IST