Skipper Steve Smith scored an unbeaten 178 as Australia were bowled out for 451 in the afternoon session on day two of the third Test against India in Ranchi.

The visitors, who resumed the day on 299-4, rode on a 191-run fifth-wicket stand between Smith and Glenn Maxwell (104) to put up a respectable first innings total.

Left-arm spinner Ravindra Jadeja claimed his eighth five-wicket haul in his 29th match to return with figures of 5-124.

Jadeja ran out last man Josh Hazlewood (0) to deny Smith any chance of getting a second double century of his career.

The captain, who started on his overnight score of 117, led by example during his marathon knock that lasted for close to four sessions.

Smith's 51-run partnership with Steve O'Keefe (25) frustrated the Indian bowlers before Jadeja and Umesh Yadav, who took three wickets, combined to finish off Australia's tail.

But it was the 28-year-old Maxwell who set the tone for the day with his maiden Test century in just his fourth Test since making his debut in 2013.

Maxwell, who started the day on 82, achieved his hundred with a boundary in the morning session before embracing Smith and kissing the badge of his helmet.

The right-hander, known more for his explosive limited-overs exploits, played a controlled 185-ball knock laced with nine fours and two sixes before falling to Jadeja.

Vice-captain Ajinkya Rahane led India after skipper Virat Kohli failed to take the field because of a right shoulder injury he suffered on Thursday.

Kohli, who picked up his injury while fielding in the afternoon session of the opening day, will bat in the crucial Test.

The four-match series between the world's top two sides is tantalisingly poised at 1-1 with India needing at least a draw to have any chance of winning back the Border-Gavaskar Trophy.