The hosts Australia was bundled out for 300 on the fourth day, which also forced them to follow-on at home for the first time in 30 years.
Virat Kohli became the first Asian captain to win Test series in AustraliaWhat's the story?
Such was the fragility of the Australian batting, a full day's play possibly could have been enough to win a record three Test matches in a single series in Australia had the heavens not opened up While Australian batting was severely handicapped due to the suspensions of their premier batsmen Steve Smith and David Warner but it can take nothing away from the heady achievement of Kohli's men, who have conquered an unchartered frontier with a lion-hearted display.
Indian sides have traditionally struggled overseas but there is now belief within the camp they can conquer any team, anywhere at any time. "The skipper had words of encouragement for the Australian team which has struggled throughout the series", the proud skipper added.
India, having failed to win a Test series in Australia in 11 previous attempts, ended a slump that dates back to when they were crushed by Don Bradman's side in 1948.
It was there, and the subsequent tour of England, that he and coach Ravi Shastri identified the attacking brand of cricket that they wanted to play, all in preparation for Australia.
For some Australians the series will always carry an asterisk given their two best batsmen, Steve Smith and David Warner, were unavailable because of bans they received for the ball-tampering scandal in South Africa a year ago. We thought we had a number of opportunities during that Test to go well ahead and when those key moments came up India outplayed us, to be honest.
It makes harrowing reading that over the last 12 months, as calculated by cricket writer Brydon Coverdale, no Australian averaged more than 32 in Tests with only one ton posted - Usman Khawaja's epic in Dubai.More news: Goerges to meet Andreescu in ASB Classic Women's Singles final
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"It is a great feeling for all of us".
If this victory is put into perspective with some of Indian cricket's famous away series wins, it will be right up there both in terms of novelty as well as quality.
Prime Minister Modi called the Test series win a "historic accomplishment".
"... Has he been his best in this series?"
"The tosses we have won, the opposition has not come anywhere close to us".
"I see this series as a stepping stone for this team to inspire the next lot of Test cricketers". Paine felt Indian batsmen stepping up and scoring runs at crucial junctures in the series is something their batsmen can learn from. "For some of the guys in their third, fourth Test maybe it's hard to look and say "I haven't scored any hundreds" but Marcus (Harris) and Travis (Head) showed, and Marnus (Labuschagne) in the first innings, that they can score runs at Test cricket".
"In Melbourne and Sydney we were outplayed in all departments". They are dictating terms now which is the most wonderful thing you can ask for from your bowlers'.