The Proteas needed 26 from 24 balls in pursuit of 177, but the wicket of Heinrich Klaasen for 52 from 27 swung a dramatic game in India’s favour.
Arshdeep Singh conceded only four from the penultimate over, leaving Hardik Pandya to defend 16 from the last.
David Miller was sensationally caught by Suryakumar Yadav at long-off for 21 from the first ball before India closed out a seven-run win.
It sparked jubilant scenes among the India players and fans in Barbados, including superstar Virat Kohli, who dragged his side to 176-7 with 76 off 59.
It is India’s second T20 title, having won the inaugural tournament in 2007, and first World Cup win in either format since the 2011 50-over competition.
For South Africa, it was a horrible defeat that brought back all the pain of