Chasing a 5-0 whitewash, Australian looked on course for more but for the last two overs from debutant Jasprit Bumrah and Ishant Sharma, which got them just seven runs in an inconsequential match at the Sydney Cricket Ground.
Opener Warner laid the foundation with 122 off 113 balls, while Marsh remained unbeaten on a brisk 102 off 84 deliveries after India skipper Mahendra Singh Dhoni asked the home team to take first strike.
Warner struck nine fours and three sixes, while found the fence nine times and cleared it twice.
Australia lost last match's centurion Aaron Finch in the first over to Ishant, following which Warner shared a half-century stand with the in-form skipper Steve Smith.
Smith's dismissal to Bumrah, his maiden wicket, was followed quickly by those of George Bailey and Shaun Marsh.
Warner then steadied the ship by putting on a valuable 118 runs for the fifth wicket with Marsh at just seven runs an over.
Then came another crucial partnership of 85 runs for the sixth wicket between Marsh and Matthew Wade (36 off 27 balls), paving the way for another big total by the home side that has already chased down two 300-plus totals in the series so far.
The visitors made two changes, bringing in Manish Pandey for the injure Ajinkya Rahane, as also handing out a surprise debut to Bumrah, the youngster not even officially included in the ODI squad.
(REOPENS FGN 7)
Bumrah got his maiden international wicket as Smith was caught at midwicket in the 12th over, off a ball that jumped high on him. At the other end, Dhawan got rid of Bailey (6) in the 15th over as Australia were under considerable pressure at that stage. 78/3 became 117/4 in the 22nd over, as Shaun Marsh (7) was run-out, the ball deflecting off Gurkeerat Mann (0-17).
While Ravindra Jadeja (0-46) bowled with control, Umesh Yadav (1-82) proved to be expensive once again.
The partnership was then broken in the 39th over, Warner caught at backward point off Ishant, and Australia were placed at 249/5 in the 40th over. Marsh then took over the finishing responsibilities and was given able support by Matthew Wade (36) as the duo pushed the score past the 300-mark in the 46th over, putting on 85 runs for the 6th wicket.
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