The political rally at the Ahmedabad stadium named after Modi hosted a "75 years of friendship through cricket" event, relegating the fourth and final Border-Gavaskar Test to a sideshow.
A potential world record crowd in the 132,000-seat capacity stadium met the leaders, likely to smash the MCG's mark for highest attendance at a day of Test cricket set in 2013.
The leaders' arrival at the stadium was slightly delayed, but once the Indian prime minister stepped foot in his own stadium, chants of "Modi, Modi, Modi" echoed around the ground as they would for cricket icon Virat Kohli.
Australia captain Steve Smith and Indian skipper Rohit Sharma met the leaders on stage, with the four linking arms and raising them in the air.
Mr Albanese then joined Mr Modi to do a lap of honour around the stadium in a hovercraft with giant bats and stumps on the back of it, waving to the delighted fans in the crowd.
Afterwards, he was asked how it differed to his previous experiences in India while backpacking.
"It certainly is (different) - it's the honour of my life," Mr Albanese told reporters.
The prime minister sang the national anthem arm-in-arm with captain Smith and the rest of the Australian team, and stayed for the start of play.
The leaders left the match after seven overs.
Mr Albanese is heading to Mumbai, where he will take part in a roundtable with Australian and Indian chief executives, promote Australian products at an expo and discuss ways to improve film-making collaborations with Bollywood.
He has made the trip with a major Australian business delegation in order to further boost trade ties.
"It's very important that we cement those ties even further. Towards the end of this year, I'm looking forward to an upgrade in the economic relationship between Australia and India," he said.
Work is under way on broadening the current Australia-India Economic Cooperation and Trade Agreement (ECTA) to include issues such as co-operation, sustainable development, digital trade and government procurement, as well as extra goods and services.
The prime minister will later visit the western naval command, which is responsible for Indian forces in the Arabian Sea, and meet with defence personnel who have taken part in exercises in Australia.
Opposition foreign affairs spokesman Simon Birmingham on Thursday welcomed Mr Albanese's comments that the relationship between the nations is at a high point.
He added India hosting the G20 summit this year would also be critical in advocating for the end of Russia's invasion of Ukraine.
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