The Aussie skipper was dismissed for 117 and declared with his team on 572-7 shortly after tea on a record-breaking second day of the fourth and final Test, before India closed on 71-1.
Smith became only the third batsman along with Don Bradman and Jacques Kallis to score centuries in four consecutive Tests ??? though he remains two behind ???The Don??? who went on to make six.
Smith also became the first man to score centuries in his first three Tests as captain, and for the first time in Test history all of Australia???s top six batsmen passed 50.
The hosts, already 2-0 up in the series, began the day on 348-2, with Smith on 81no and Shane Watson on 56no.
Watson fell for 81, throwing his wicket away when he was caught by Ravi Ashwin at deep midwicket off the bowling of Mohammed Shami ??? missing out on his fifth Test ton.
It was the 24th time he had made a Test half-century but failed to go on and reach triple figures.
Smith reached his eighth Test ton off 168 balls when he smashed a full toss from Indian fast bowler Umesh Yadav for a boundary.
Yadav gained a small measure of revenge when he dismissed Smith just before the interval, finding the edge off an attempted drive and giving wicketkeeper Wriddhiman Saha a simple catch.
Shaun Marsh (73) and Joe Burns (58) then piled on the agony for India, adding 114 for the fifth wicket.
Marsh, run out for 99 in the drawn Melbourne Test, also missed out on a hundred when he was caught behind off Mohammad Shami.
Burns, playing in his second Test, registered his first 50 with a composed display, highlighted by nine boundaries.
He fell in the deep to Shami, the fast bowler???s fourth wicket. Ryan Harris smashed Bhuvneshwar Kumar for 19 runs in an over and brought the crowd to their feet with his knock of 25 from just nine balls and when he gave Shami his fifth wicket, Smith declared.
India were given 25 tricky overs to negotiate, and their reply got off to a terrible start, Murali Vijay going to the third ball of the innings, nicking Mitchell Starc behind.
But Lokesh Rahul (31no) and Rohit Sharma ??? who hit two sixes on his way to 40no ??? played well to get to the close without further damage being done.