The Windies went into the last over needing 19 to win and with expert death bowler Ben Stokes handed the ball, it looked like England would see out the win.
But Brathwaite held his nerve to fire the Windies to an unlikely four-wicket win with two balls to spare, leaving Stokes devastated on the field.
“To see Carlos play like that at his debut World Cup was just tremendous,” an emotional West Indies skipper Darren Sammy said afterwards.
England captain Eoin Morgan refused to blame Stokes.
“It’s not his fault, we’re all in this together, we enjoy our wins, and the pain will be shared tonight,” he said.
Marlon Samuels anchored the West Indies’ run chase of 156 with an unbeaten 85, including nine boundaries and two sixes, after England had posted 155-9 in their 20 overs.
After being reduced to 11 for three, Samuels single-handedly kept the Caribbean team in the hunt with his 66-ball blitz.
Brathwaite finished on 34 not out off just 10 balls as the 2012 champions completed a hat-trick of titles after the women’s clinched their maiden trophy earlier on Sunday.
The Under-19 team had already lifted the youth World Cup in February.
“Everybody in the West Indies is a champion,” beamed Sammy.
The Windies also became the first team to lift the World T20 twice.
England’s batting hero Joe Root had hit Windies hard with a double strike when he shared the new ball with David Willey to get the West Indies’ openers trudging back to the dug out.
Root struck on his first ball as Johnson Charles skied a catch to mid-wicket but the really big wicket came on the third delivery when Chris Gayle departed.
Gayle tried an ambitious slog after hitting a first-ball boundary but could only find the fielder at long-on to trigger wild celebrations in the English camp.
Willey then got semi-final star Lendl Simmons out leg before wicket for nought to leave the Windies tottering at 11 for three.
– Samuels unbeaten 85 –
Samuels counter-attacked by hitting Chris Jordan for three boundaries in the sixth and last over of the powerplay that cost England 16 runs.
Samuels, who was given an early life after wicketkeeper Jos Buttler grassed a caught behind, stitched a 75-run partnership with Dwayne Bravo (25) to help the Windies rebuild.
Willey turned up for his second spell with a double strike to hurt Windies’ hopes of reviving their chase as the asking-rate kept growing, but new man Brathwaite had other ideas.
Brathwaite managed an unbeaten 54-run stand with man-of-the-match Samuels to stun England.
“I can’t really express how much of a top knock (by Samuels) that was. We couldn’t turn back, it was a question of when not if,” said Brathwaite.
Bowling coach Curtly Ambrose was overjoyed.
“We believe we can chase any target because we’ve got some real firepower,” said the fast bowling legend.
“We believe we can chase any target because we’ve got some real firepower.”
Earlier West Indies’ bowlers justified captain Darren Sammy’s decision to field first as Samuel Badree and Andre Russell put England on the backfoot at only 23 for three in 4.4 overs.
Opening the attack for the Windies, leg-spinner Badree got Jason Roy clean out for a second ball duck and also accounted for struggling English skipper Eoin Morgan (5) in his third over.
Root (54), who struck his third half-century of the tournament, and Buttler (36) then came up with a fine re-building act to manage a 61-run fourth wicket partnership.
Medium-pacer Brathwaite got Buttler against the run of play when Bravo took a good catch at deep mid-wicket before celebrating with his customary ‘Champions’ dance.
Sammy soon cashed in on Bravo’s catch to bring him on to bowl and the medium-pacer obliged with two wickets in his second over.
England’s batting soon crumbled after Brathwaite got dangerman Root trudging back as a scoop shot turned out to be the in-form batsman’s undoing.
Braithwaite and Bravo shared three wickets apiece to hit England hard.
David Willey’s late cameo of 21 was studded with a boundary and two sixes and to give the England total some respect.