Marsh's 99-run innings was studded with 11 fours and two sixes as he took Australia's lead to 383 runs at the Melbourne Cricket Ground after rain delayed play twice in the morning session.
Australia declared their innings at lunch and India now have to score 384 runs in 70 overs across two sessions of play to remain alive in this four-match series.
Play started early by 30 minutes to make up for the time lost on day four, but only three balls into the day and rain came down to stop the proceedings. There was a 40-minute delay before resumption of play again.
India looked like they were waiting for the declaration to come about, while Australia were looking to play for time as the pitch didn't show enough variable bounce like in Brisbane or deterioration like in Adelaide.
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It resulted in a slow morning as the 50-run partnership for the 8th wicket came up off 112 balls. The 300-mark for Australia came up in the 92nd over.
When play resumed, Harris was the first to depart of the two batsmen, caught behind off Mohammad Shami (2-92). There were only 20-odd minutes left in the session as Nathan Lyon (1*) came out to bat, but probably with the message that the team management intended to declare at the break.