Pappachan Pradeep scored the winner a minute before half-time with a powerful right-footer from the top of the box that caught a diving Syrian goalkeeper Musab Balhous on the wrong foot.
Some 10,000 home fans at the overflowing Ambedkar stadium cheered loudly when the final whistle blew to signal a rare moment of triumph for Indian football.
It was the first defeat in the tournament for Syria, ranked 122 in the world against India's 151, after they had won all four round-robin matches.
"The boys deserved to win because they worked very hard for the tournament," said India's English coach Bob Houghton.
"The atmosphere in the team is excellent and we just loved the support we got from the crowd. It's a great night for Indian football."
Cambodia, Kyrgyzstan and Bangladesh were the other teams in the tournament.