Yuvraj Singh played a match-winning innings as India, roared on by their supporters in Ahmedabad, knocked holders Australia out of the World Cup.
Ricky Ponting's 104, his first century for 13 months, guided a misfiring Australian batting line-up to 260-6.
It was a target that looked within India's compass, and Sachin Tendulkar's 53 set the hosts off in fine style.
Gautam Gambhir added 50 before Yuvraj (57 not out) saw India to a five-wicket win with 14 balls to spare.
The result ended an extraordinary run of success for the Aussies in the World Cup. Beaten finalists in 1996 when Ponting was a junior player, they won the next three tournaments, an imposing run that included a run of 34 matches without defeat.
But their fallibility was shown up by Pakistan, who beat them in their final group match of this tournament, and India's strong batting line-up proved too powerful for Ponting's men.
 | Australia are not a subtle team anymore, they relied on pace and their pacemen were not quite disciplined enough. What a selection Raina proved, he was pretty nerveless in that vital partnership, and Yuvraj can do no wrong
Test Match Special's Vic Marks |
The co-hosts did come under pressure when tossing away middle order wickets two-thirds of the way through their chase. But Yuvraj and Suresh Raina (34) pushed India across the line with a terrific partnership of 74 from just 61 balls.
India's next match is sure to be a huge occasion - a semi-final in Mohali against Pakistan next week.
Yuvraj said afterwards: "The pressure was something else, I knew there was Suresh yet to come and I knew if we could get a partnership we could take the game to the end. We just played it straight and used the pace.
"People say it's just another game, but beating the three-time champions I feel is really special for me and our team."
Ponting commented: "We competed hard, there's no doubt about that. 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. Yuvraj and Raina played too well. We needed to get into their tail and weren't able to do that.
"It's disappointing to be bowing out now. I wish India well for the rest of the tournament."
Singh hails 'special' win over Australia
Australia won the toss and opted to bat first. The new ball was shared by the excellent left-arm seamer Zaheer Khan and off-spinner Ravichandran Ashwin, who found plenty of turn.
Shane Watson and Brad Haddin weathered the early dangers before Watson attempted a slog-sweep against Ashwin in the 10th over, missed and was bowled.
The biggest stand of the innings followed, with Haddin joined by his skipper Ponting, and the two right-handers addied 70 in 13 overs.
Haddin played at a lovely tempo throughout, combining delicate nudges with some muscular smites, but departed for 53 when trying to loft Yuvraj through the covers and picking out Raina at extra-cover.
Ponting began his innings tentatively, unsurprisingly for someone with a previous tournament best of 36, but he moved his feet nicely to put Yuvraj away for two on-side boundaries and was soon threatening something substantial.
Australia did not 'deserve' to win - Ponting
Yuvraj picked up a second wicket when Michael Clarke's ugly swipe ballooned to deep mid-wicket, and when Mike Hussey and Cameron White departed cheaply to the accurate Zaheer, Australia's ambitions were duly lowered.
On 91, one ball after launching Harbhajan Singh over mid-off for four, Ponting was given not out by umpire Ian Gould when India's most experienced spinner appealed for lbw. The decision may well have been reversed if India had not already used both their reviews, but Ponting went on to complete his fifth World Cup century.
Much of Australia's most effective biffing at the death was provided by David Hussey (38 not out from 26 balls) but it was hard to call a clear favourite during the break between innings.
When Tendulkar hit the first two legitimate balls he received for fours - the first a delicate nudge behind point, the second lifted over the slips off Shaun Tait - the home fans began to believe early on that it would be their night.
 Figures show percentage of balls bowled in designated areas (BOAL=back of a length) |
Virender Sehwag was bounced out by Shane Watson for just 15, but the Tendulkar and Gambhir stand of 50 in exactly 10 overs put India in good shape.
There was to be no 100th international century for Tendulkar - though he did pass 18,000 runs in ODIs and become the tournament's leading run scorer - as a fast delivery from Shaun Tait brushed his outside edge en route to Haddin. There was an anxious pause for the bowler while the umpires checked whether he had cut the return crease with his back foot.
Gambhir and Virat Kohli played the spinners so comfortably in India's next partnership that suddenly things began to look a little desperate for the Aussies, but they got a huge lift when they were gifted their next two wickets.
Kohli hit a knee-high David Hussey full toss to midwicket before Gambhir was run out when Yuvraj failed to respond to his call for a quick single - the third such breakdown in communications between the two batsmen.
When Mahendra Dhoni lashed a square cut off Lee to backward point, Clarke diving to claim an excellent catch, India still needed 74 to win from 12.3 overs with five wickets to win.
Another wicket would have put Australia firmly in control but instead Yuvraj and Raina played some of the boldest cricket of the day.
The 40th over, bowled by Lee, went for 14 and brought the crowd alive once again. Yuvraj raised his half-century from just 54 balls as Ponting looked for an inspired bowler to win him the match.
Lee, in what will surely be his last appearance for Australia, could not produce that inspiration. Instead he was lofted nonchalantly for a straight six by Raina.
Aside from providing the wicket of Tendulkar, Tait let down his captain with a barrage of wides, and Johnson was lacklustre.
The makeshift spin unit had tried its best and failed - and it was left to Yuvraj to hit the winning runs as he nailed a lofted cover-drive for four off Lee.
City governor Shintaro Ishihara made the declaration following his re-election for a fourth term.
