Travis Head smashed a breezy 49 not out as Australia quickly reeled in their small target to wrap up the third Test against India well inside three days in Indore, ending the hosts' nine-match unbeaten run at home.
Friday's nine-wicket romp was only Australia's second win in their last 18 attempts in India and also saw the tourists seal a place in the World Test Championship final in June.
India will set themselves up as Australia's opponents in that final if they win the fourth Test in Ahmedabad next week.
Australia, who now trail the four-match series 2-1 after being outplayed in Nagpur and Delhi, began day three needing just 76 runs to seal the win but had to do so on a pitch where 30 wickets had tumbled in the first two days.
They got off to the worst possible start, losing Usman Khawaja before even making a dent in their target.
Ravichandran Ashwin removed the opener caught behind for a duck with the second ball of the day and Khawaja burned a review trying to overturn that decision.
Head saw no point in retreating into a shell and counter-attacked to lift the pressure, hitting Ashwin for a six, and suddenly boundaries started flowing.
Marnus Labuschagne, who made 28 not out, sealed the victory with a boundary as Australia romped home in 18.5 overs.
Steve Smith, leading Australia in the absence of regular skipper Pat Cummins, who returned home to be with his ailing mother, called it "a complete performance" by his team.
"That first day, losing the toss and having to bowl first ... our bowlers just got the ball in the right areas and put India under pressure," Smith said.
"Yesterday, India fought back with the ball and we had to toil hard. Nathan (Lyon) got all the rewards with eight wickets but I think our bowlers as a collective were really good.
"Obviously, we're thinking of Patty back home but I've really enjoyed this week, I like captaining in this part of the world, I think I understand the conditions really well."
Lyon's match haul of 11 wickets saw him named Player of the Match.
India captain Rohit Sharma said they were on the back foot after being bundled out for 109 in their first innings.
"We understand how important it is to put runs on the board in the first inning," Rohit said.
"If we'd batted well in the first innings, things might have been different.
"We need to regroup, and understand what we did right in the first two Test matches. No matter what the pitches are, we need to come out and do our jobs."
The final Test is scheduled to begin in Ahmedabad next Thursday.
