Batting first, India scored a decent 295 for six in 50 overs with Virat Kohli scoring a run-a-ball 117 en route his 24th ODI century.
In reply, Australia never looked in trouble as they knocked off the required runs with 1.1 overs still remaining.
Glenn Maxwell put paid to India's hopes of an elusive win with a superlative 96 off 83 balls that had eight fours and three sixes as the bowlers once again undid the valiant effort from the batting unit. The fielding was also not upto the mark at times.
Aaron Finch (21 runs, 23 balls, 3 fours) and Shaun Marsh (62 runs, 76 balls, 6 fours) started off at almost six runs per over and the rate didn't come down even with early bowling changes.
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Debutant Gurkeerat Singh Mann dropped Finch in the 6th over, with the batsman on 20. But it had yielded a wicket, with Finch caught behind in the 8th over off Ishant. Steve Smith (41 runs, 45 balls, 5 fours) then came to the crease and started off without feeling any pressure.
Against the run of play then, in the 19th over, Ravindra Jadeja (2-49) got one to spin away from him, and he edged it to slip with Ajinkya Rahane happily accepting the catch. His dismissal brought India back into the game with George Bailey (23) stumped in the 27th over.
Dhoni showed another quick thinking and brilliant glove-work moment when he ran out Mitchell Marsh (17) off an Umesh Yadav (2-68) throw in the 36th over. In between, Shaun Marsh was out caught pulling off Ishant in the 30th over. And when Matthew Wade (6) holed out against the same bowler in the 39th over, Australia were reduced to 215/6.
Maxwell had reached his half-century in the 40th over, run-a-ball and there was an element of doubt about a faint edge on the snickometer in that same over.
But then he took 15
runs off the 43rd over by Yadav
changing the momentum of the game. Thereafter, the equation came down to a very manageable run-a-ball, and the duo took Australia home -- and to the series win -- without much fuss.
Earlier, Kohli's hundred guided India to 295/6 in 50 overs. He put on 119 runs with Shikhar Dhawan (68 runs, 91 balls, 9 fours) and another 109 runs with Ajinkya Rahane (50 runs, 55 balls, 4 fours, 1 six), but the Men in Blue had to settle for a below-par score.
R Ashwin and Manish Pandey were excluded from the playing eleven as skipper MS Dhoni went in with six bowlers. Australia won the toss and elected to field, bringing back Mitchell Marsh to the line-up and leaving out Joel Paris.
Rohit Sharma (6) and Shikhar Dhawan took first strike then, but the former couldn't replicate his centuries from the first two matches and was out caught behind off Kane Richardson (1-48) in the fifth over.
Kohli then walked to the crease, and looked fluent from the very beginning. It was important in the context of the innings as Dhawan was scratching around for his runs. While they didn't lose any more wickets, India could only reach 62/1 in the first 15 overs.
Electing to bat, India lost for their openers, Rahul and Murali Vijay inside five overs with 22/2 when Pujara and Kohli calmed the proceedings dishing out an array of elegant ground strokes.
Making a hurried return after he was pulled in from an ongoing first-class match, Rahul got out for duck edging Stuart Broad to Ben Stokes at the third slip.
Vijay looked in fine nick and hit four boundaries en route to reach personal milestone of 3000 runs but could not fend off a rising delivery from Anderson that took off from his gloves and looped to Stokes at gully.
In the same match, Jayant had made his ODI debut and today the Haryana offspinner was handed India's 286th Test cap by former India captain Ravi Shastri.
That senior pro Gautam Gambhir was making way for a fit-again KL Rahul was already made clear by Kohli as India made two changes to their XI.
England were bolstered by the return of Anderson in place of Chris Woakes who's down with knee injury.