Pujara (1,000* balls in 166.4 overs this series) became just the fifth Indian Test batsman, after Dravid (1203 balls - 2003/04), Vijay Hazare (1,192 balls - 1947-48), Kohli (1,093 balls - 2014-15) and Sunil Gavaskar (1,032 balls - 1977-78), to have faced 1,000 or more balls in a Test series in Australia.
Josh Hazlewood (2-51) struck early on a wicket with a greenish tinge to remove Rahul but that only brought Pujara to the crease.
At stumps on day one, they were 303 for four with the rock-like number three not out 130 and Hanuma Vihari on 39.
While debutant Mayank Agarwal displayed a commendable knock on his maiden worldwide outing, the experienced pair of Cheteshwar Pujara and Virat Kohli ensured the Indian cricket team does not lose their momentum.
Agarwal continued his impressive introduction to test cricket with another half century.
The International Cricket Council (ICC) on Tuesday rated the MCG pitch where the third Test between India vs Australia was played as "average", brightening the prospect of play in the ground.
Shortly after, Pujara reached his century off 199 balls with a boundary off Starc to fine leg. It is the first time the 30-year-old has scored three hundreds in a series.
At 303/4 on the opening after deciding to bat first, the visitors won the first-day honours and would like to bat themselves into further position of strength on Friday to ensure a result (draw or win) that will more or less ensure a maiden Test series victory for India Down Under.
Australian squad: Aaron Finch (c), Usman Khawaja, Shaun Marsh, Peter Handscomb, Glenn Maxwell, Marcus Stoinis, Mitch Marsh (vc), Alex Carey (vc), Jhye Richardson, Billy Stanlake, Jason Behrendorff, Peter Siddle, Nathan Lyon, Adam Zampa.
Maligned for much of his 83-Test career, Lyon is now among the first players picked in Australia's squad having taken 335 wickets at a career average of just under 32.