Pakistan was dismissed for 231 in the last over chasing 261 to beat the pre-tournament favorites.
The 28,000 fans inside the Punjab Cricket Association Stadium went wild in celebrations, shouting, dancing and waving national flags after India carved out a memorable victory against its traditional rival in the presence of the Prime Ministers of both countries.
Pakistan had done well earlier to peg India back to 260-9 despite some sloppy fielding, with left-arm pace bowler Wahab Riaz taking a career-best 5-46.