Mahendra Singh Dhoni's side had looked in all manner of trouble when reduced to 55 for five at the start of the 16th over after winning the toss and electing to bat, but Karthik (146 not out off 140 balls) and Dhoni (91 off 77) put on a stunning 211-run partnership to help India reach 308 for six from their 50 overs.
Australia's reply never got going as Yadav ripped through their top order, taking figures of five for 18, as they subsided to 65 all out - by comparison their worst score in a one-day international is 70.
Adam Voges was the only man to offer any resistance before being the last man out having made 23.
Earlier in the day Australia's opening bowlers Clint McKay and Mitchell Starc were rewarded for their nagging line and full length with two wickets apiece to put India in difficulty.
But Karthik, fresh from his ton in the previous warm-up against Sri Lanka, and Dhoni carefully rebuilt the innings before going on the offensive during the final 20 overs.
The pair took a particular liking to James Faulkner and Mitchell Marsh as they plundered boundaries at will, with their partnership coming off just 192 balls.
Yadav then ran through the Australian batting, taking all five wickets to reduce them to 28 for five.
There was no recovery from there and Ishant Sharma chipped in with three for 11 to help seal victory.
It capped a bad day for Australia, with captain Michael Clarke set to head to London for specialist treatment on his lower-back injury.
- Sports & Recreation
- Mahendra Singh Dhoni