The Virat Kohli-led India fought back after the morning session to send back the openers but Shane Watson (10 not out) and captain Steve Smith (28 not out) did well to not only stitch an unbeaten 38-run partnership but also maintain the scoring rate at above four in the second session as well.
Warner was the first to go just post the lunch break but not after registering his third hundred in this series and 12th overall.
Rogers departed in the very next over when the left-hander got a thick inside edge of Mohammed Shami (1-49) and the ball crashed on to the stumps.
Watson and Smith then played intelligent cricket to not only blunt the Indian attack but also score runs at a good pace.
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Earlier electing to bat on a hot and sunny morning, the Australian opener made merry against an Indian attack that once again lacked steam.
Lokesh Rahul dropping Rogers, was on 19 then, off Shami did not help matters for the visiting side as the openers took Australia to 123 for no loss at lunch.
On an emotional day for the Australian team, which is playing their first match at this venue where late Phillip Hughes was fatally struck by a bouncer six weeks back, the hosts made sure that tributes translate into performance as well.