Head scored a magnificent 152 and Smith a gritty 101 at the Gabba in Brisbane to put Australia into a strong position to go 2-1 up in the five-Test series.

With rain forecast over the next three days, India seem to have virtually no chance of winning the match and can only realistically hope for a draw.

After all but 13.2 overs of the first day were washed out on Saturday, India started strongly Sunday with three wickets in the first hour.

But Head and Smith batted India out of the game despite a superb spell from pace spearhead Jasprit Bumrah (5-72) after tea with the second new ball.

At the close of play, Alex Carey was on 45 and Mitchell Starc was on seven.

Head, who hadn't scored a run in his previous three innings at the Gabba, looked to be playing on a different surface to his teammates.

While the other Australian batsmen struggled, Head came out firing, smashing an increasingly demoralised Indian attack to all parts of the ground.

The visitors bowled a lot straighter to Head than they did in Adelaide -- where he hit a sparkling 140 in a big Australia win -- but he was watchful early and punished any loose deliveries.

He brought up his century off 115 balls and his 150 off 157, hitting 18 fours in the process.

Smith's innings was in stark contrast to Head's.

He looked badly out of touch early, playing and missing multiple times and was lucky to survive several lbw shouts.

But as his innings progressed he looked more and more confident, playing with far more fluidity once he passed 50. 

He brought up his 33rd Test century and his first in 18 months to a rapturous reception from the big Gabba crowd.

He fell soon after, edging Bumrah to Rohit Sharma at first slip with the score on 316.

Australia had resumed the day at 28-0 and lost the wickets of Usman Khawaja (21), Nathan McSweeney (9) and Marnus Labuschagne (12) in the extended first session.

But Head and Smith's magnificent partnership put India firmly on the back foot until Bumrah struck back with the new ball.

He was head and shoulders above the other Indian bowlers, who pitched too short for long periods, and had his fourth wicket when Mitchell Marsh was caught by Virat Kohli at second slip for five.

One run later Head finally departed, edging Bumrah to wicketkeeper Rishabh Pant to leave Australia 327-6.