After starting day two of the Boxing Day Test at 6-311, Australia added another 73 runs without losing a wicket on Friday morning.
Smith brought up a ton in back-to-back Tests when he drove Nitish Kumar for four midway through the first session of the day.
Captain Pat Cummins (41no) is also adding valuable runs, sharing an unbeaten partnership with Smith that is heading towards three figures.
The 35-year-old arrived at the MCG coming off scoring his first Test century since June 2023 when he hit 101 in the rained-out match at the Gabba.
It was Smith's 11th Test century against India, adding to his 12 tons made in the Ashes.
Smith overtook England star Joe Root (10) for the most Test centuries against India.
It was also Smith's fifth Test century at the MCG, a venue where he averages more than 80.
The former Australia captain seemed to be facing his cricketing mortality after making a combined 19 runs across the first two Tests of the Border-Gavaskar series.
It extended his drought without a Test century into 18 months.
Continuing on from an unpredictable start to the Test, play was briefly interrupted on Friday morning when a pitch invader wearing an Indian shirt ran onto the field and touched Rohit Sharma and Virat Kohli.
Security eventually got to the man, but not before Kohli was forced to awkwardly interact with him.
It came after teenager Sam Konstas smashed an unforgettable 60 to begin his international career on Thursday, bravely taking on India's strike weapon Jasprit Bumrah.
Usman Khawaja (57) and Marnus Labuschagne (72) also made starts, making it the first time Australia's top-four had all passed 50 in the same innings since the first Test in Pakistan in March 2022.
Cummins won his first toss of the series, electing to bat first to escape the sweltering conditions on Thursday when the temperature soared to 39C.
The MCG has become a bowler-friendly venue since Scott Boland's famous debut against England in 2021.
Only two totals of more than 300 have been posted across the three Boxing Day Tests prior to this one.
Kohli, who Konstas idolised growing up, was fined 20 per cent of his match fee for his shoulder bump on the 19-year-old.
A villain of the Australian crowds this summer, India fast bowler Mohammed Siraj fired off words to Konstas multiple times.
Sam Konstas hit the third-quickest half-century by an Australian Test debutant on day one at the 'G. (AP PHOTO)
"I was just trying to get in the contest and whoever I was facing, just trying to bring the best version of myself," Konstas said.
"Obviously it got a bit heated at times, which was good for me.
"Just feel like that brings the best out of me, and hopefully I go well next innings."
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