Australia has completed a sensational victory over India in Pune, stunning the hosts in less than three days to win by 333 runs.

As it was on day two, Steve O'Keefe stole the show with the ball and Steve Smith led the way with the bat as Australia pulled off the most unlikely of runaway Test wins.

O'Keefe took another haul of 6-35 — the exact same figures he managed in the first innings — in the second innings, finishing as man of the match with the remarkable figures of 12-70.

Those figures are the 10th best in the history of Australian Test cricket, and better even than Shane Warne's best Test figures of 12-128.

The New South Welshman was near enough to unplayable after lunch, setting batsmen up with big turners before sliding through defences with straight balls.

This plan was most brilliantly executed to remove India's captain Virat Kohli, with the superstar shouldering arms to a delivery that went straight on and into the off stump.

Kohli's wicket was a death knell for India, whose top order had already been wiped away by O'Keefe and Nathan Lyon.

Murali Vijay (2) and KL Rahul (10) were both adjudged to be out LBW, but both reviewed the decisions to no avail.

O'Keefe's wicket of Virat Kohli was decisive. ( AP:Rajanish Kakade )

Kohli's wicket brought upon another collapse. Ajinkya Rahane (18), Ravi Ashwin (8) and Wriddhiman Saha (5) all fell to O'Keefe, and the die was well and truly cast.

The tail mustered no fight, Australia's victory long since confirmed too.

Skipper shows rising team the way

Smith picked up where he left off early on day three, mastering the difficult conditions to bring up one of the finest centuries in a Test career that is growing more storied by the match.

On a pitch no other batsman looked comfortable on, Smith hit India's spinners around with ease as Australia established a match-winning lead.

Steve Smith's ton in tricky conditions must rate among the very best of his career. ( Reuters: Danish Siddiqui )

Smith was not without some good fortune, dropped a number of times and surely out LBW had India been able to review the call. He more than made the most of his luck though.

He would fall for 109, caught in front of the stumps by a skidding delivery that would prove foreboding for O'Keefe's spell to come, but his job was well and truly done.

Smith was well supported by Mitch Marsh (31) and Mitch Starc (30), but his century stood out in a match of starts and failures.

His runs would prove to be more than enough as India failed to muster any fourth-innings challenge at all.