England were strong favourites to lift the crown with the Caribbean side needing 19 off the last six balls of the match.
But Brathwaite launched an audacious assault on Ben Stokes, heaving him over the ropes four times in a row to seal a four-wicket success and pen a stunning denouement.
In an ill-tempered contest, played out in front of 66,000 rapt Indian fans, West Indies celebrated victory ecstatically, as Stokes sat crumpled in the middle.
Marlon Samuels played a brilliant anchor innings of 85 in 66 balls - having been reprieved on 27 when a low catch by Jos Buttler grazed the turf - but he needed Brathwaite’s brute force to finish the job with 34 in just 10 deliveries.
That Yorkshire’s Joe Root was on the losing side is a near travesty.
He bailed his side out from a rocky start with 54 hard-fought runs and then took an unlikely starring role with the ball, dismissing Chris Gayle and Johnson Charles in a dizzyingly effective one-over experiment.
That gave England confidence that their 155-6 was enough and, in truth, they seemed ahead of the game for most of the West Indian pursuit.
But this is a heavy-hitting side who do not know when they are beaten and Brathwaite’s blows saw them become the tournament’s first-ever two-time champions.
Windies skipper Darren Sammy won the toss and decided to chase, but the plan stalled at the outset.
After David Willey sent down a tight first over, Eoin Morgan unveiled his high-stakes gamble: Root from the High Court End.
He had only bowled one over, for 13 runs, in the previous five matches but he is the kind of player that thrives on the biggest stage.
His first ball was full enough to tempt Charles, who hit an arcing drive neatly into Stokes’ hands at long-on.
Root’s fists pumped, his team-mates swarmed and Gayle crossed with the departing batsman.
The next ball went for four, uppish but clear of point, and the third was tossed up full again.
Gayle could not allow the chance to pass but he only got half of it and Stokes raced into position to pouch another catch.
It was a seismic moment, as the entire stadium and one dejected Jamaican surrendered to Root’s magnetism.
The celebrations had only just faded when Willey reignited them, hooping a delivery into Lendl Simmons for a regulation lbw.
Eleven for three turned into 37-3 by the end of the powerplay - Samuels peeling off four boundaries to stabilise the ship.
Samuels was given out off Liam Plunkett on 27 but Buttler had not taken a low catch cleanly and he was recalled.
Dwayne Bravo had a reprieve too, substitute fielder Sam Billings dropping him on 11, before Adil Rashid struck with his final delivery. Root, somewhat predictably, was underneath it.
The 15th over swung for the Windies, Samuels smearing Plunkett for two sixes and a four, but the 16th was England’s - Willey returned and had the big-hitting duo of Andre Russell and Sammy caught in the deep.
Both were sent on their way, the skipper with a pointed rendition of the ‘champion’ thrust - the Caribbean side having annoyed England with their own performances in the field.
In the end it fell to Stokes and Brathwaite, the latter landing four knockout blows in row, one flicked over fine leg and three drilled between straight.
Earlier, England - sent in having lost the toss - lost Jason Roy, Alex Hales and Morgan cheaply.
Roy, England’s explosive catalyst in India, lasted two balls, leaving a gate between bat and pad and paying with his leg stump.
Hales was guilty of carelessness, turning a modest Russell delivery to short fine-leg - but Morgan was torrid.
Ten of his 12 balls were dots and it probably helped England when he nicked Samuel Badree to slip.
When the sides met in Mumbai the leg-spinner took 0-34; here he reeled off 2-16 in four overs.
All the while Root was maintaining a cool head, stroking two early fours through cover, taking the only boundary off Badree.
He found his perfect foil in Buttler (36), who smashed Sulieman Benn for three sixes down the ground before holing out.
Root’s salvage job continued as he reached 50 in 33 balls but Bravo conjured a brisk double strike, deceiving Stokes and strangling Moeen Ali.
And the West Indies got their real target in the 15th over, Root’s mishit lap just carrying to Benn in the ring. As the Windies leapt and danced, Root offered a few choice words in response.
Willey steered the tail to a crucial 38 in the last four overs, pounding two sixes in a punchy 14-ball cameo.
It was good, but Brathwaite’s effort was better.