Cheteshwar Pujara scored his third century of the series as India took control on day one of the fourth and final Test against Australia.
The 30-year-old, who scored 123 in the first Test and 106 in the third, finished the day on 130 not out as the tourists closed on 303-4 in Sydney.
Hanuma Vihari ended 39 not out with India, who lead 2-1, needing a draw to clinch a first series win in Australia.
Josh Hazlewood was the pick of the Australian attack with 2-51, but the rest of the bowling unit laboured on a hot day in Sydney.
He removed Rahul in his first over, the opener nicking a delivery to Shaun Marsh at slip.
Agarwal and Pujara put on 116 for the second wicket before the former tried to smash a Nathan Lyon delivery for six and was caught at long-on by Mitchell Starc.
Captain Virat Kohli (23) and Ajinkya Rahane (18) both made starts before being caught behind by Tim Paine but Pujara continued to frustrate the Australian bowlers to complete his 18th Test century.