Cheteshwar Pujara caught all eyes on the second day too, falling eventually for 193 while Rishabh Pant hit his second Test century and also the second overseas.
At the interval, Pujara was 181 not out with Rishabh Pant unbeaten on 27, sharing a 60-run partnership at the Sydney Cricket Ground as India continued its tried and tested approach this series of building successive partnerships to grind Australia's bowling attack down.
When Australia bat, they will have a new look opening pair with Usman Khawaja padding up with Marcus Harris after the underperforming Aaron Finch was axed. Previously, Farukh Engineer, with a score of 89 at an Adelaide Test, had the highest score for an Indian wicket-keeper in Australia.
After seeing Pujara dropped by Khawaja his previous over, spinner Nathan Lyon finally got his man his next over, deceiving Pujara in flight and seeing the batsman chip a simple return catch to the bowler to end his nine-hour innings.
Australia and India cricket teams met Australia Prime Minister Scott Morrison on Tuesday on the eve of the fourth Test in Sydney.
"When you're looking towards a World Cup - he's certainly re-invented himself in the T20 format but for one day format, I'm just interested in that one. I thought they drove it into us pretty well".
"That sort of set the scene for Rishabh Pant to come in and show his skill".
"Every hundred which is scored in global level is special for me because I have just started my career", Pant said.
But Agarwal and Pujara vindicated India captain Virat Kohli's decision to bat first by showing plenty of steel on a pitch offering plenty of bounce and carry. "I only think about one thing of what the team needs from me, that's the only goal I have". "They have worked extremely hard for three-and-a-half Tests to get us to where they want us today".
Pujara brought up his 150 with a boundary and seemed destined for his fourth Test 200 before attempting to whip Lyon down the leg side. His partner, Hanuma Vihari got out early in the day for a well-made 42.
India have never lost a Test when Kohli has won the toss - winning 18 and drawing three - and he had no hesitation in opting to bat in Sydney.