The dashing left-hander struck 60 runs off 43 balls as the 2007 champions posted 159 for seven before skittling Australia for 86 in 16.2 overs at the Sher-e-Bangla National Stadium.
Off-spinner Ravichandran Ashwin claimed four for 11 as Australia's powerful top order imploded and only three batsmen got to double figures before succumbing to their third successive defeat in a tournament they began as one of the favourites.
"I certainly don't think that our batters can hold their head particularly high in terms of their shot selection, match awareness, their game sense..." Australia captain George Bailey told reporters.
"I guess this is the most disappointing game of late from this team," said Bailey, who was "embarrassed" by his own performance in the tournament.
For Australia, Glenn Maxwell top-scored with 23, hitting three towering sixes before departing when Australia needed him most.
Aaron Finch and David Warner failed to give them a flying start, Cameron White disappointed in his first match of the tournament, Shane Watson failed to do justice to his reputation and Bailey also flopped.
The Indian spinners claimed seven of the 10 wickets, once again exposing Australia's frailties against slow bowling.
It was a highly satisfying outing for India captain Mahendra Singh Dhoni whose team had already qualified for the last four.
India did not drop a single catch, Ajinkya Rahane and Mohit Sharma got a game, the middle order was tested and, above all, persisting with the struggling Yuvraj paid off.
The architect of India's 20-over (2007) and 50-over (2011) World Cup triumphs, Yuvraj showed glimpses of his vintage form, hitting five fours and four sixes.
"It was a brilliant innings, the way he paced it," said Dhoni, who shared an 84-run stand with Yuvraj.
"An innings like this was needed for him, when he can be expressive. He just needed to be himself. It was an ideal opportunity. He went in, played a few deliveries and then expressed himself.
"We all know the kind of batsman he is. He can clear any ground in the world. (It) doesn't matter whether (it's) a fast bowler or a spinner bowling.
"Initially he may struggle in the first five or seven deliveries. Your good luck is if you get him out, if not he will take you out of the game."
Image: Yuvraj Singh
Photograph: Scott Barbour/Getty Images
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