India failed to build on centuries from Shikhar Dhawan and Virat Kohli as a dramatic collapse saw them crumble to a 25-run defeat that handed Australia an 18th consecutive completed one-day international victory on home soil.
The tourists were on course to pull a game back in the five-match series, which Australia were leading 3-0, when Dhawan and Kohli took the score to 277 for one in the 38th over in pursuit of 349 in Canberra.
But the pair departed in quick succession during a collapse that saw India lose their last nine wickets for just 46 runs, Kane Richardson claiming his maiden ODI five-wicket haul, to be dismissed for 323.
While Warner fell seven runs short of a century, becoming one of four expensive victims for Ishant Sharma, Finch went on to complete a 97-ball ton.
Finch departed for 107, mis-pulling Umesh Yadav to mid-on, but Steven Smith and Glenn Maxwell helped Australia smash 110 from the final 10 overs.
Skipper Smith blasted 51 from just 29 deliveries, including four fours and three sixes, while Maxwell contributed a 20-ball 41.
Smith’s decision to hand Nathan Lyon the new ball then backfired, the off-spinner taken for 23 in two overs, and India had 65 on the board after eight overs when Rohit Sharma nicked Richardson down leg to depart for 41 off 25 balls.
Dhawan and Kohli then made batting look easy under lights, hitting 126 and 106 respectively, the latter’s second successive hundred, to leave their side requiring 72 from 75 deliveries for victory.
But Richardson and John Hastings shared five wickets for just 17 runs in 23 balls to decimate India before the former and Mitchell Marsh finished things off.