Australia won the toss and decided to bat at Rajiv Gandhi International Stadium as the teams began to mark the home stretch for the 50-over World Cup.
But the decision didn't pay off as India finished on 240-4 in 48.2 overs in reply to Australia's 236-7.
Jadhav scored 81 not out off 87 balls, including nine fours and a six, while Dhoni made 59 not out off 72 deliveries. The pair put on 141 runs for the unbeaten fifth wicket after coming together on 99-4 in the 24th over.
Australia won the preceding Twenty20 series 2-0.
Western Australia's Ashton Turner made his ODI debut and he replaced D'Arcy Short from the T20 lineup. Jhye Richardson also missed out while leg spinner Adam Zampa (2-49) played instead of spinner Nathan Lyon.
Skipper Aaron Finch played his 100th ODI for Australia.
India opted for only one wrist spinner in Kuldeep Yadav, with Ravindra Jadeja partnering him.