Suresh Gutgutia, 57, complained of chest pain on Saturday when Indian seamer Ashish Nehra came on to bowl the last over with Pakistan needing nine runs to win, the Press Trust of India reported on Sunday.
Gutgutia, an industrialist based in the Eastern Indian city of Dhanbad, was rushed to hospital where he was pronounced dead by doctors.
Nehra kept his nerve and conceded just three runs in his over to seal a five-run victory, but Gutgutia could not take the suspense and failed to see India's sensational win, his relatives said.
India went 1-0 up in the five-match One-day series with the win at Karachi's National Stadium.
India are on their first full tour of Pakistan in almost 15 years, playing only a short three-match One-day series across the border in 1997.
They are due to play three Test matches after the One-day series.