Chetan Sharma registered the first ever World Cup hat-trick, as he accounted for Ken Rutherford, Ian Smith and Ewen Chatfield with the last three balls of his sixth over.
All three were clean bowled, as New Zealand were dismissed for 222.
India needed to chase the target in 42.2 overs, but thanks to some sensational batting from Kris Srikanth and Sunil Gavaskar, they reached the target in just 32.1 overs.
