This was India’s first victory in a Test series in Australia, in 12 Test series going back to 1947-48.
This was India’s first victory in a bilateral ODI series in Australia. This was only the second such series, Australia having won the first in 2015-2016.
If you count ODI series with more than 3 teams, India had won the Commonwealth Bank series in 2007-08, where Australia was the losing finalist and Sri Lanka was the third participant.
And there was the B & H World Championship in 1984-85, where Pakistan was the losing finalist and all 7 Test teams of that period took part. India won all 5 of their matches, and the series was immortalized by Shastri’s Audi.
India did not win this T20I series, which was drawn 1-1 with one “no result”. However India had won the only other 3-match series in 2015-16 3-0. That was the only time that a visiting team had made a clean sweep of any series in Australia in a series of 3 or more matches in ANY format of cricket.
The worst defeat for Australia at home would appear to be England’s 2-0 victory in the 1886-87 Test series. Or perhaps England’s 5-1 victory against a Packerized team in 1978-79.
To put it differently, this was the first time that Australia failed to win a series in ANY format of cricket during a tour. Perhaps they will have better luck with Sri Lanka in the latter half of their season. Sri Lanka is to play 2 Tests and no other matches.
While many teams have separate captains for Tests, ODIs and T20Is, India had Virat Kohli as captain in all 3 formats.His counterpart was TD Paine in Tests and AD Finch in ODIs and T20Is.