Australia quietened the wild support from the 100,000-strong home crowd by dismissing their previously unbeaten opponents for 240 before Travis Head's sensational century meant they romped to victory with seven overs to spare.
After their bowlers expertly took advantage of a slow pitch, Australia were themselves reduced to 47-3 as India hit back in an electric new-ball spell.
But Head and Marnus Labuschagne calmly weathered the storm with a stand of 192 as Indian hope drifted away from the world's largest cricket stadium.
Head was caught for 132 from 120 balls with just two runs needed, but Glenn Maxwell flogged the winning runs a ball later while Labuschagne ended 58 not out from 110.
The superb victory means Australia extend their record as the most successful side in 50-over World Cup history and now sit four titles clear of the rest of the pack.
It also caps a six-month period in which they beat India to win the World Test Championship and retained the Ashes in England.
India, meanwhile, were left crestfallen as their bid for a first white-ball title since 2011 - an achievement which looked unstoppable as they made rampant progress through the semi-final and group stage - fell at the final hurdle.
One of Australia's greatest nights
This was supposed to be India's day in front of an enormous home crowd with their prime minister Narendra Modi, who this stadium is named after, up in the stands.
Instead, it ended in crushing disappointment as Head produced one of the great World Cup knocks and Australia ran out surprise and comfortable winners.
By the time 29-year-old Head reached his century, some in the vast stands had already made their exit, while seamer Mohammed Siraj was in tears at the end.
Australia were contenders when this tournament began, without being tipped by many to go all of the way, just like when they won the 2021 T20 World Cup.
Their campaign hit serious jitters early on with defeats in their opening two games, first by India and then South Africa, but they have won the title with nine consecutive victories, beating every team in the tournament in a row.
At the end, their players, including England's old foes David Warner and Steve Smith, charged onto the field in celebration.
Australia may have won it all before, but this ranks as one of their greatest nights.
Head ends India's dream
Head did not play in the first four games of Australia's campaign because of a broken hand, but Australia kept him in their squad, knowing the match-winning quality he possesses.
He scored 109 in his first appearance against New Zealand but this innings was on another level as he first dealt with intense pressure before punishing the bowling.
After his opening partner Warner nicked the first ball of the chase through the slips, Head crashed two boundaries to settle Australian nerves.
Warner then edged a wide ball to slip for seven off Mohammed Shami, while Mitchell Marsh and Steve Smith both fell to the brilliant Jasprit Bumrah.
The crowd was alive again at that stage, although Smith's lbw decision would have been overturned had he reviewed.
Those wickets came in a manic opening period in which India took the upper hand but also gave up 15 extras in the powerplay alone, those in blue seemingly too eager to defend their low score.
Batting became easier on a slow pitch that had offered more turn in the day, and Head took advantage. He cracked 14 fours and four sixes, with the sixes all pumped high over mid-wicket.
On 99 he would have been run out as he scampered to three figures, had Ravindra Jadeja's throw hit from cover.
He was finally out for 137, caught at deep mid-wicket attempting to finish in style. As he left the field he was embraced by Labuschagne and was congratulated by the Indians with the result already decided.
Superb Aussies tie down India
Head's innings will take the headlines, but this victory was built on a sensational performance with the ball and a brave decision to bowl first at the toss by Pat Cummins.
Captain Rohit Sharma gave India a rapid start with 47 from 31 balls, but from 76-1 in the 10th over, Australia applied a stranglehold on India's star-studded batting line-up and did not let go.
Head played a crucial hand too, brilliantly catching Rohit as he ran back from cover, before Shreyas Iyer was caught behind off Cummins four balls later to leave the hosts 81-3.
That left Virat Kohli and KL Rahul to attempt a rebuild, but the canny Australia bowlers kept the scoring to a crawl through a mix of short, slower balls and athletic fielding, all while captain Cummins mixed his pack to great effect.
Kohli and Rahul put on 67 in 109 balls before the former captain played on to Cummins for 54 in the 29th over to leave the vast stadium stunned in silence. Rahul then nicked a beauty from Starc, ending any real hope of a significant India score.
India's lower order had hardly been needed in this tournament, and when finally called upon, Ravindra Jadeja managed only nine and Suryakumar Yadav 18 with just four boundaries coming after the first 10 overs.
India's worst performance with the bat came at the worst possible time in the tournament, but huge credit must go to Cummins and his champion attack.
'We saved our best for last' - what they said
Australia captain Pat Cummins: "We saved our best for last and a couple of big-match players stood up and we're pretty chuffed.
"We were desperate in the field, I thought it all started against South Africa last week. The boys were fantastic. We've got an ageing squad but we are still throwing ourselves around. We were really chuffed with 240 because we were happy with anything under 300."
India captain Rohit Sharma: "We were not good enough today but I'm really proud of the team and how we played from game one. We tried everything we could from our side but it wasn't supposed to be.
"We were looking at 270 or 280 but then we kept losing wickets. We couldn't get a partnership together and that is exactly what Australia did to win the game, they stitched a good partnership after they lost three wickets."
Player of the match, Australia's Travis Head: "Not in a million years did I think that would happen [being man of the match today and in the World Test Championship final]. What an amazing day. I'm just thrilled to be a part of it.
"It is a lot better than being sat on the couch at home! I'm very lucky that everything went well and I was able to get back and the support that the boys showed, I didn't think this would happen. I was nervous in the first 20 balls but Marnus [Labuschagne] batted brilliantly and it is great to bat with him. It was an amazing partnership."
Former England bowler Steven Finn on BBC Test Match Special: "Everything, from start to finish, that Australia did was outstanding.
"They were truly outstanding in the field again. Australia were just on top from that moment that Travis Head caught Rohit Sharma and they never let India off the hook."
-BBC
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