Dhoni was given tremendous support from Kedar Jadhav with a belligerent unbeaten 61 from 57 balls in a match-winning 121-run stand.
India successfully chased down a target of 299 set by Australia who scored 298 for nine with Shaun Marsh scoring 131 off 123 balls.
The part-time spinner's action raised concerns among the match officials about its legality after the match in Sydney.
Rahul and Pandya were axed ahead of India's opening ODI against Australia in Sydney on Saturday
The Australians made 288 for five off their 50 overs after winning the toss and restricted India to 254 for nine.
The announcement comes hours before the start of the first one-day international of a three-match series against Australia starting Saturday in Sydney
"It's just an opportunity to see Alex play in a position he's done quite bit of now in Big Bash and one-day cricket," said fellow opener Finch
It is another blow for Marsh who was axed from the Test squad to play Sri Lanka, along with his brother Shaun.
The BCCI gives bonuses for major tournaments like the World Cup or Champions Trophy but extra payments for a bilateral series is rare.
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