West Indies needed 19 runs in the 20th over which Brathwaite (34 not out) provided in style by smashing Ben Stokes for sixes off the first four balls.
Marlon Samuels lifted the team with 85 not out as West Indies finished on 161-6 in 19.4 overs.
Earlier, Brathwaite took 3-23 to help restrict England to 155-9.
The 2012 champion West Indies become the first team to win the World Twenty20 title twice.
For 2010 champion England, Joe Root produced an allround performance of 54 and 2-9.
England sets 156-run target for West Indies in WT20 final
Joe Root produced a defiant knock of 54 as England scored 155-9 against the West Indies in the World Twenty20 final on Sunday.
Root struck seven fours off 36 deliveries in his fourth T20 half-century and was involved in a 40-ball 61-run stand for the fourth wicket with Jos Buttler (36 off 22).
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But England failed to build other lasting partnerships in the face of tight bowling from the West Indians.
Legspinner Samuel Badree did the early damage with a spell of 2-16 with the new ball while Carlos Braithwaite (3-23) and Dwayne Bravo (3-37) bowled fine spells later.
The winner of this final will become the first team to win a second World Twenty20 title after England won in 2010 and the West Indies in 2012.
West Indies bowls first against England in WT20 final
West Indies captain Darren Sammy won the toss Sunday and decided to bowl first against England in the World Twenty20 final.
Both teams went in unchanged in a game that will see the winner become the first team to win a second World Twenty20 title.
In the semifinals, England beat New Zealand by seven wickets at New Delhi and the West Indies got past pre-tournament favorite India by the same margin at Mumbai.
The West Indies and England played each other earlier in a Group 1 game in which opener Chris Gayle had clobbered a 48-ball 100 not out to power the West Indies to a six-wicket win.
England was the champion in 2010 while the West Indies won the tournament in 2012.
India (2007), Pakistan (2009) and Sri Lanka (2014) are the others to have won the tournament.
