Under-fire skipper Steve Smith cracked a gritty century as he combined with the recalled Glenn Maxwell to give Australia the opening day honours in the third Test against India in Ranchi Thursday.

The visitors were 299 for four at stumps after electing to bat first in their 800th Test at a venue which is hosting its first ever five-day international, with Smith unbeaten on 117 and Maxwell on 82.

Smith, at the centre of a major row after being accused by India of systematically abusing the decision review system (DRS) in the last Test, put on 159 runs with Maxwell to lift Australia from 140-4.

Indian fast bowler Umesh Yadav claimed two wickets while spinners Ravindra Jadeja and Ravichandran Ashwin took one each.

The 27-year-old Smith brought up his 19th Test century with a boundary off Murali Vijay, raising his bat to the acknowledge the generous applause of the home crowd.

Smith, who crossed the 5,000-run mark in his 52nd Test, became the first Australian captain to score two hundreds in a series in India. He hit 109 in the opener in Pune.

West Indies' Clive Lloyd (1974-75 and 1983-84) and England's Alastair Cook (2012-13) are the only other international captains to have scored two or more centuries during a series in India.

At the other end Maxwell, who was drafted into the XI in place of injured Mitchell Marsh, changed gears after reaching his fifty with a six off Ravindra Jadeja.

Maxwell, playing his fourth Test, smashed 5 fours and 2 sixes as he took the attack to the opposition in the final session of play.

The stand between Smith and Maxwell is Australia's best for the fifth wicket in India, surpassing the 145-run partnership between Michael Clarke and Matthew Wade during the second Test of the 2013 series.

Meanwhile India skipper Virat Kohli injured his right shoulder while fielding and went off the field in the 40th over, leaving Ajinkya Rahane to lead the side for the rest of the day.

Kohli fell awkwardly while trying to save a boundary at long-on and instantly left the field while clutching his shoulder. He was seen putting on ice packs in the dressing room.

Earlier Smith, who hit 13 boundaries in an otherwise sedate knock, put on 51 runs for the fourth wicket with Peter Handscomb (19) after Australia lost three wickets in the morning.

Opening batsman Matt Renshaw (44) gave the visitors a brisk start before undoing his hard work by edging a wide Yadav delivery, with Kohli taking the catch at first slip.

Renshaw and David Warner had put on 50 runs for the opening wicket before left-arm spinner Jadeja struck in his first over to get Warner (19) trudging back to the pavilion.

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