Smith is yet to be dismissed in the series and was unconquered on 110 at lunch.
Mitchell Johnson pounded a whirlwind half-century and was 67 off 53 balls as Australia went to the interval at 351 for six, trailing the tourists by 57 runs.
The pair had put on an unbroken 104 runs for the seventh wicket as the game began to slip away from India’s grasp after they went into the third day with a 187-run lead.
Smith, who took over the captaincy after Michael Clarke injured his right hamstring in the first Adelaide Test, was the fifth Australian skipper to score a century in his first Test as captain.
Monty Noble, Clem Hill, Lindsay Hassett and Chappell all scored hundreds in the first innings of their debut Test as skipper with Chappell the last against the West Indies at the Gabba in 1975.
India began the third day well with two wickets inside the opening hour but Johnson’s lusty hitting quickly swung the game Australia’s way.
Smith, who was not dismissed by India in last week’s Adelaide Test win with scores of 162 and 52, continued to be the bane of the tourists with another defiant knock. He has scored 324 runs so far in the series.
Johnson was winning his own little war with the Indians, who bowled short and sledged him early in his innings only to fire up the Australian fast bowler.
He cracked 10 fours and a six to back up his skipper after the dismissals of Mitchell Marsh and Brad Haddin.
Marsh did not offer a shot and was bowled for 11 by Ishant Sharma, probably expecting a higher bounce.
Speedster Varun Aaron grabbed a big wicket with a vicious throat ball on the first delivery after drinks that Haddin could only fend away to bat-pad where Cheteshwar Pujara took an easy catch for six.
Aaron got an official warning from umpire Ian Gould for bowling three short-pitched balls in the same over. (AFP)