India's first innings folded for 465, adding just three runs to their overnight score, with Mitchell Johnson polishing off the tail without much fuss.
The hosts then rode on David Warner's pacy 40, Rogers' patient 69 and Shaun Marsh (62 not out) to reach 261-7 at close on a rain-hit fourth day at the MCG, taking an overall lead of 326 with three wickets in hand.
Interestingly, England is the only team to have successfully chased down a total of 300 plus on the fourth innings at MCG. They had made 332 for seven way back in 1929.
At stumps, Shaun Marsh and Ryan Harris were batting on 62 and 8 respectively.
Earlier, resuming at an overnight score of 462/8, India could survive just 15 deliveries as Johnson dismissed Mohammed Shami (12) and Umesh Yadav (0) within a space of eight balls to earn Australia a 65-run lead.
After he was dismissed by Ashwin, Rogers and Shane Watson (17) tried to extend the lead as Australia took lunch at 90 for one in 22 overs.
However, rain intervention after lunch, resulted in a loss of 85 minutes of play and when play resumed, regular wickets fell to leave the hosts at 174/4 in 43 overs at tea, which was taken after an extended second session.
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