India's victory by an innings and 135 runs is their sixth-largest in Tests, and their second-best against Australia - they'd won by an innings and 219 in Kolkata in 1998. All of those six wins have come in the subcontinent - four in India and two in Bangladesh.
MS Dhoni has won 22 of his 45 Tests, the most by an Indian - Sourav Ganguly had won 21 out of 49. Seventeen of Dhoni's 22 wins have been in home Tests, where he has a 17-3 win-loss record in 26 matches. Mohammad Azharuddin is the next-best at home, with a 13-4 record. In away Tests, though, Dhoni's won only five out of 19 Tests, which is joint-second with Rahul Dravid (five out of 17). Ganguly won 11 out of 28 overseas.
Australia have lost at least two Tests in five of their last six series in India. During this period, South Africa, England and Pakistan all have better win-loss records in Tests in India.
This is the 11th instance of a team losing a Test after declaring in its first innings, but the first in which the team declaring has lost by an innings. The only other such instance for Australia was in the famous Headingley Test of 1981, when they declared at 401 for 9 in their first innings, and eventually ended up losing by 18 runs.
After an opening partnership of 56, Australia's next nine wickets put together only 75, their second-lowest ever against India (in innings in which they've been bowled out). Their only poorer effort was in the MCG Test of 1981, which they lost by 59 runs. In the fourth innings of that Test, Australia's last nine wickets put together 72.
Leaving aside the openers, the highest score by the other nine Australian batsmen in their second innings was Michael Clarke's 16. Only twice against India have Australia's nine batsmen from No.3 to No.11 had a lower top-score, in an innings in which they've been bowled out. In Mumbai in 2004, and in Delhi in 1969, the top-score by the non-openers was a run lesser.
Australia's batting average of 25.35 so far is their lowest in a series against India in which they've played at least two Tests.
R Ashwin's 5 for 63 in Australia's second innings is his eighth five-for, in his 14th Test. Only nine Indian bowlers have taken more five-fors. Among Indian bowlers who've taken at least eight five-fors, Ashwin's rate of 1.75 Tests per five-wicket haul is easily the best; the next-best is Subhash Gupte's 12 in 36 matches, a rate of one every three Tests.