Australia lost the first three ODIs of the series to concede an unassailable 3-0 lead but regained some pride with a 21-run win in the fourth match at Bengaluru.
They would have wanted to gain some momentum with another victory ahead of the three-match Twenty20 series, starting on Saturday, but a clinical performance from India barely gave them an opportunity.
Sharma and Ajinkya Rahane, who completed his third consecutive half-century, gave India a rollicking start with an opening stand of 124 before the latter was out for 61.
It was Sharma's 14th hundred in the 50-over format and he brought it up with a massive six over mid-wicket against paceman Nathan Coulter-Nile.
The stylish right-handed batsman, who had scored 71 and 65 in the last two matches, hit 11 fours and five sixes in his 109-ball knock.
Sharma and captain Virat Kohli (39) added 99 in their second wicket partnership to take India to the brink of victory before both were out caught in the deep in the same over to leg-spinner Adam Zampa.
Earlier, Australia failed to build on a solid start from their openers and finished on 242 for nine after winning the toss and opting to bat.
David Warner followed up his match-winning knock of 124 in the last ODI with a fine 53 and added 66 with Aaron Finch in a brisk opening stand.
All-rounder Hardik Pandya dismissed Finch for 32 to break the dangerous stand, who had combined in a partnership of 231 to set up Australia's win in the last encounter.
Australia were moving along nicely at 100-1 but then suffered a mini collapse, losing captain Steve Smith, Warner and Peter Handscomb in quick succession to be reduced to 118-4.
India's spinners pulled back the scoring rate with left-arm spinner Axar Patel the most devastating, finishing with three for 38.
India pace duo Jasprit Bumrah (2-51) and Bhuvneshwar Kumar also bowled accurately during the closing overs to restrict Australia, and made up for their average opening spells.
(Reporting by Sudipto Ganguly in Mumbai; editing by Christian Radnedge)
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