Yuvraj hit 60 off 43 balls to steer India to 159-7 after they were sent in to bat, before Australia collapsed in spectacular fashion to be bowled out for a paltry 86 in 16.2 overs.
India, who had already qualified for the semi-finals, topped group two of the Super-10s with four successive wins. They will meet the number two team from the other group next Friday for a place in the final.
It was Australia's third loss in a row, leaving them at the bottom of the table along with Bangladesh.
Pakistan, who beat Bangladesh by 50 runs earlier on Sunday, will clash with the West Indies on Tuesday to decide the second semi-finalist from the group.
South Africa have made it to the knock-out round from group one, while Sri Lanka will face New Zealand in Chittagong on Monday to determine the other semi-finalist.
Indian captain Mahendra Singh Dhoni said he was not surprised at the ease with which Yuvraj batted after a poor run earlier in the tournament.
"We all know what kind of a player Yuvi is and this T20 format is ideal for someone to get back into form," Dhoni said. "He gave himself time to get set at the start and then he opened out.
"There was no dew at all which helped the bowlers grip the ball well. It was a really good effort in the field. We now need a good rest before the semi-final."
India, whose previous three wins came while batting second, were given first strike by Australian captain George Bailey and found themselves in immediate trouble.
India's top order faltered after opener Rohit Sharma fell to part-timer Brad Hodge off the fourth ball of the innings and slipped to 66-4 by the 12th over.
Left-handed Yuvraj, who made one and 10 in the two innings he got to bat in the tournament, launched a spectacular counter-attack that included five boundaries and four sixes.
Dhoni made 24 during a fifth-wicket stand of 84 off 42 balls with Yuvraj before he was bowled by Mitchell Starc in the penultimate over.
Australia's batting caved in under lights at the Sher-e-Bangla stadium with Glenn Maxwell emerging the top scorer with 23.
Eight batsmen failed to reach double figures against the steady Indian spin attack in which leg-spinner Amit Mishra supported Ashwin with two wickets for 13 runs.
Bailey said he was disappointed at the way this tournament was going for his Australian team.
"I don't think we have been fans of the way we have been playing," he said. "There was a lack of game sense on a number of occasions. I just hope we can play well against the hosts on Tuesday."
...........................................................................................................................................................
COMMENTS (8)
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ
@Sami-ul-Haq: yeah .... obviously ..... our financial strength is so much ki hum kisi ko bhi khareed sakte hai...... and bikne waalon mein pakistan tops the list .....:) those with no finance and beggars desperate for money :D
@Sami-ul-Haq: Same australia which almost won the match lost 7 wickets in 20 odd runs.
And you think that match is not fixed. Pakistan is the only country whose players were sent to jail for fixing. Ask Imran Khan and he will tell you thing or two about fixing culture in Pakistan team since ages.
I can understand that you cannot accept good bowling strength of India but calling it fixing is insulting to both India and Australia
i am gonna sue u for ur irresponsible remarks.btw pray to allah that Pak doesn't meet India again in the tournament otherwise u know what wud happen ?
@ Sami ul haq of course whenever india looses they are terrible players and whenever they win the match is fixed right? Jealousy/prejudice/bigotry has no bound for some people. Now even Australian team is currupt. Wow Btw why are you watching indian matches, don't you have your own team? Focus on your country matches than obsessing over ours.
In this T-20 tournament the Indian bowling has been excellent while Pakistan's batting has also been good. Usually it is the opposite!! Wishing both the sides luck for the remainder of the tournament.
Sami-ul-Haq Brilliantly worded comment!
Awesome performance by indian bowlers. They looks best bowling side in this tournament.
Totally fix match - even sirilanka umpire was giving wrong decisions for stumping and no ball