(CNN) -- Yuvraj Singh held his nerve to steer India into the last four of the World Cup and end Australia's 12-year reign as champions.
Yuvraj struck a vital 57 not out to ensure co-hosts India reached their target of 261 with more than two overs to spare and book a semifinal clash with Asian rivals Pakistan.
Earlier, captain Ricky Ponting had hit an imperious 104 and Brad Haddin a quickfire 53 as Australia reached a competitive total of 260-5.
But half centuries from Sachin Tendulkar and Gautam Gambhir edged India towards their target before Yuvraj and Suresh Raina propelled them over the line.
After the game Yuvraj told Sky Sports: "The pressure was something else. People say it's just another game, but beating the three-time champions I feel is really special for me and our team."
Defeat came as a bitter blow to Ponting, who has had to field questions about his future both as player and captain throughout the tournament, but he later insisted he wouldn't be stepping down.
"We competed hard, there's no doubt about that," he said. "We thought we were in with a chance at the half-way stage, and that we had a reasonable total.
"But we didn't bowl as well as we needed to, we needed more wickets from the middle order. It's disappointing to be bowing out now. I wish India well for the rest of the tournament."
Australia made a quick start to their innings as Haddin and Shane Watson put on 40 but it was with Ponting's arrival at the crease that the impetus began to grow.
Despite a shaky start, Ponting soon punished some wayward Indian bowling to record his first century in 13 months, and despite Michael Clarke, Mike Hussey and Cameron White going cheaply David Hussey added a valuable 38 as Australia made 260-5.
India reached 44 in their reply before Virender Sehwag fell but Tendulkar (53) and Gambhir (50) continued the charge with a partnership of 70 before the batsman known as "the little master" was dismissed by Shaun Tait.
When Virat Kohli and Indian captain MS Dhoni were removed in quick succession, Australia could sense the game changing.
But Yuvraj showed plenty of character to lead his side home, despite the calamitous run out of Gambhir. Raina added a vital 34 and when Yuvraj smashed the winning runs it sparked wild scenes of celebration in Ahmedabad.
Meanwhile, England spinner Michael Yardy has flown home from the World Cup because he is suffering from depression.
The 30-year-old, who took two wickets during his three games at the tournament, said on the England and Wales Cricket Board's website: "Leaving at this stage of the World Cup campaign was a very difficult decision to make.
"But I felt it was the only sensible option for me and I wanted to be honest about the reason behind that decision."
Hugh Morris, the managing director of England Cricket, said: "I would like to offer my full support to Michael on behalf of everyone involved with the England team and the ECB.
"Michael has been an integral part of the England set-up in recent years and while he will be missed in the knock out stages of the World Cup, our priority now is to ensure that he returns home to his family and is able to spend time recovering with a strong support network around him."