Chasing an imposing 360 to win in Jaipur, India went past the target for the loss of just one wicket and with six overs to spare.
It was the second highest score to win a 50 overs international, only beaten by the astonishing 436 runs by a South African side in Johannesburg in 2006, with Australia again the unfortunate opposition.
Openers Rohit Sharma (141 not out) and Shikhar Dhawan (95) put India on their way before the more experienced Virat Kohli completed the task with a brutal innings.
Kohli smashed 100 not out off just 52 balls, including seven sixes and eight fours.
It was the fastest century by an Indian in one day internationals and the seventh quickest off all time.
India’s score of 362 was the highest ever in this form of the game for the loss of just one wicket and it enabled them to level the series at 1-1.
Australia had looked strong favorites to take a 2-0 lead after amassing a formidable score on a superb batting wicket.
Each of their top five batsmen scored a half century, with captain George Bailey top scoring on 92 not out.
But the visiting bowling attack was powerless to prevent India racing to victory, with Sharma at first leading the way.
India are the current world champions in 50 overs cricket, helped to victory on home soil in 2011 by national hero Tendulkar.
He quit the shorter form of the game last year and announced his retirement from all cricket last week.
Tendulkar will play his final Test match on his home ground in Mumbai next month against the West Indies, completing 200 appearances at this level.