Australia recorded their 1000th international victory. Australia had won their first-ever international match against England in March 1877.
MS Dhoni becomes fifth cricketer to score 10,000 ODI runs for India.
Paceman Jhye Richardson took four for 26 as Australia finally gave their fans something to smile about with a 34-run victory over India in the first one-day international on Saturday despite a magnificent 133 from Rohit Sharma.
It was only a fourth win in 20 one-dayers going back to June 2017 for world champions Australia and came at the same Sydney Cricket Ground where their first home test series loss to India was sealed on Monday.
The home batsmen, led by Peter Handscomb's 73, posted a competitive 288 for five off their 50 overs and when India stumbled to four for three inside four overs, it looked like being a rout.
Rohit, who missed the final Test to go home for the birth of his first child, celebrated his return to the tour with a 138-run partnership with Mahendra Singh Dhoni (51) to get the innings back on track, however, and while he was batting, India had a chance.
Australia, wearing a retro canary yellow kit, won the toss and skipper and opener Aaron Finch decided to bat only to depart for a meagre six runs.
Usman Khawaja (59), on his return to one-day internationals after nearly two years, put on 92 for the fourth wicket with Shaun Marsh (54), however, and Handscomb and Marcus Stoinis (47) cashed in at the end.
Left-arm finger spinner Kuldeep Yadav was the pick of the Indian bowlers with 2-54 but it was the Australian seamers who were to leave the most decisive mark on the contest.
Debutant Jason Behrendorff removed Shikhar Dhawan in the first over and Richardson drove home the advantage by sending Virat Kohli and Ambati Rayudu back inside three balls.
Rohit, though, would not be cowed and he clubbed a huge six -- one of six in his 129-ball innings -- to move into the seventies before reaching the hundred mark for the 22nd time with two runs behind square.
His celebration of a seventh ton against Australia was subdued as there was still plenty of work to do and once he holed out to Glenn Maxwell in the deep off the bowling of Stoinis, the match was effectively over.
Richardson also removed Ravindra Jadeja and Dinesh Karthik for his best bowling figures in ODIs and the tourists finished on 254-9.
"I'm very pleased," said Finch. "We knew that they would try and take it deep and luckily we were able to take wickets and stem the flow.
"Anytime you get a team three down so early and three big guns is very important. The youngster Jhye is full of confidence and he's some pace."
India were without KL Rahul and Hardik Pandya, who were suspended and sent home pending an pending an inquiry into comments they made about women on a TV show this week which have been condemned as sexist.
"We're not very pleased with the way we played," said Kohli. "That wicket was about 300-plus par. I think Rohit played outstandingly well and MS supported him but I thought we could have done better with the tempo of the game and we fell short."
SCORES IN BRIEF
AUSTRALIA: 288 for 5 in 50 overs (Khawaja 59, Marsh 54, Handscomb 73; Kumar 2-66, Yadav 2-54)
INDIA: 254 for 9 in 50 overs (Sharma 133, Dhoni 5; Behrendorff 2-39, Richardson 4-26, Stoinis 2-66)
Result: Australia won by 34 runs.
Player-of-the-match: Jhye Richardson.