Smith scored 192 off 305 balls to spearhead Australia to 530 and then took a fine low diving as the tourists were 108-1 at stumps on the second day, trailing by 422 runs.
India's first goal will be to reach the follow-on target of 331, while the Australians – leading the four-match series 2-0 – will be pressing for victory over the final three days.
Murali Vijay passed fifty for the fourth time in the series and remained unbeaten on 55 with Cheteshwar Pujara not out on 25 at stumps after Smith swooped to take a catch low at second slip to dismiss Shikhar Dhawan for 28 off Ryan Harris.
It could have been even better for Australia but wicketkeeper Brad Haddin, who had earlier scored his first half-century in 14 innings, dropped Pujara on 12 off Josh Hazlewood.
Smith dominated day two with his highest Test score and was the last wicket to fall when he went for an extravagant shot but missed a straight delivery, which crashed into middle stump.
It was Smith’s third century of the series, his fifth for the year, and was replete with all his quirky shot-making to leave India skipper MS Dhoni at a loss as to how to contain him.
"I feel pretty good at the crease. Everything is working for me at the moment and the most pleasing thing is that we've got 530 runs on the board and that's a very good first innings total for us," said Smith. “It was pretty fun to be honest. It was nice to be able to play a few shots there at the end and try and get the total up as high as we could.”
The 25-year-old bettered his previous highest score of 162 not out in the first Adelaide Test by dancing down the wicket to plonk spinner Ravi Ashwin high into the stands.
Smith has now accumulated 567 runs in the series at an average of 189. The new skipper was aided by Haddin (55), Mitchell Johnson (28) and Ryan Harris (74) as Australia took apart the Indian attack early on the second day.
Like his captain, pacer Harris also brought up his highest Test score with a six off Ashwin, but the Indian spinner seemed to be upbeat about his team’s chances.
"We looked to get them out pretty early this morning. Unfortunately, Smith batted really well and they got too many runs for our liking," said Ashwin. "But if you look at the overall game, the score is pretty par for this wicket. It seems slow and pretty flat as well.
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