Electing to bat on a hot and sunny day, the hosts rode on a 200-run opening stand between Warner (101), registering his third ton in the series, and Rogers (95) to once again expose a toothless Indian attack.
After a strong opening show, Shane Watson (61 batting) and captain Steven Smith (82 batting) ensured that Australia stay on the saddle by stitching a 144-run unbeaten third wicket partnership on what turned out to be a frustrating day for the Indians at the SCG.
Rogers though got an early reprieve after Lokesh Rahul dropped the left-handed batsman at second slip off Mohammed Shami (1-58). The opener was on 19 and made full use of the 'life'.
Warner, who was one of the players to witness the freak accident on November 25 at this venue, was in control from the very start and slammed his 12th Test century after lunch.
India though struck back after the first session by sending back the openers in quick succession but Smith and Watson had other ideas.
Smith notched up his 10th Test half-century while Watson recorded his 24th fifty in the longest format to deny India any more celebration in the day.
Ravichandran Ashwin (1-88) got Warner back in the pavilion after inducing a leading edge to gully where Murali Vijay made no mistake.
From then on it was a case of leather hunt for the Virat Kohli-led side, which stayed on the field for 43 overs without a wicket.
India though got another chance of getting a wicket but Ashwin let Watson's edge fly past him at first slip off Umesh Yadav (0-97) on the penultimate ball of the day.
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