Joe Root's England need to win at least two more tests to qualify for the final, which will be held at Lord's in June. New Zealand have already qualified.
"This will take a while to sink in," said former India captain Bishan Singh Bedi, who hailed the win as "by far the greatest comeback in the history of Indian cricket."
A poll conducted by International Cricket Council (ICC) on their Twitter page, where it asked the best captain among Khan, Kohli, South Africa's Ab de Villiers and Australia's Meg Lanning.
As many as 536, 346 votes were casted, which the former Pakistan captain won by bagging 47.3 per cent of the votes.
There will be a new-look attack with Umesh Yadav out of the series after hurting his calf and T. Natarajan called up as a replacement. India were already without injured regulars Mohammed Shami and Ishant Sharma.
Tailenders Starc (14 not out), Pat Cummins (22) and Hazlewood (10) showed stiffer resistance than a number of their batting team mates to push Australia to 200 for the first time in the series.
Kohli lifted the 2011 World Cup and the 2013 Champions Trophy with India, before inspiring their first Test series victory on Australian soil two years ago.
It ended one of the 32-year-old's most important Test innings, having come to the crease with India in trouble at 64 for three to steer them into a strong position.
But Cummins finally got the wicket he deserved when Gill, who added 17 to his overnight score after being preferred as opener to the axed Prithvi Shaw, got a nick and Paine took a simple catch.
Lyon said the paltry 36 runs India scored in the second innings in Adelaide last Saturday was no reflection on the quality of the touring side, recalling that he was part of an Australian team bowled out for 47 in South Africa in 2011.
The visitors were skittled for a humiliating 36 in their second innings -- their lowest Test score of all time -- to lose the day-night game in Adelaide by eight wickets inside three days.
"For us, it's about being able to adapt to different conditions... you can take inspiration from the past but I don't think that guarantees anything and we have to stay in the present."