Khan struck a sublime 103 from 84 deliveries that was generously peppered with nine boundaries and two sixes
Australia remain the world's top-ranked Test team, the International Cricket Council said as it apologised for briefly and "erroneously" listing India as number one.
India demolished Australia by an innings and 132 runs in the first Test in Nagpur, and on Wednesday the ICC showed the hosts as taking over at the top of the Test rankings.
The ICC subsequently clarified that Australia were in fact still number one in Tests. India top the Twenty20 and one-day rankings.
"The ICC acknowledges, for a short period of time on February 15, 2023 that, due to a technical error, India were erroneously displayed as the No.1 Test team on the ICC website," it said.
"We apologise for any inconvenience caused."
The second Test starts on Friday and India will have history on their side at Delhi's Arun Jaitley Stadium — previously Feroz Shah Kotla — where they haven't lost a Test since 1987.
But coach Rahul Dravid said they will not get carried away by records and will focus on the coming five days of action.
"We don't look at previous history and go back in time," Dravid told reporters.
"We cannot get carried away by that. Australia are an experienced team and have good players who know they want to come back."
India hammered Pat Cummins' Australia inside three days during the first match to move closer to securing their berth in June's World Test Championship final at The Oval in London.
They need to win the series 3-1 or 3-0 to make the final.
Returning batsman Shreyas Iyer has joined the squad for the second Test after a back injury made him miss the opener.
Dravid said a completely fit Iyer will walk into the XI.
"We will assess it and tomorrow as well, when he comes in for a light hit and see how he feels," said Dravid.
"But certainly if he is ready to take the load of a five-day Test match, then without doubt, with his performances in the past, he will walk straight into the side."
Skipper Rohit Sharma led from the front in Nagpur with his 120 in India's 400, followed by key knocks from left-handed all-rounders Ravindra Jadeja and Axar Patel.
"Ability to put pressure back on bowlers made the difference and that's what Rohit did," Dravid said.
"That's what Axar and Jadeja did very well during that partnership. It is not the only way you can play but in these conditions, being able to put pressure back is important."
Khan struck a sublime 103 from 84 deliveries that was generously peppered with nine boundaries and two sixes
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