Sunil Chhetri (10th minute) and substitute Robin Singh (65th) scored for the winners while Tolgay Ozbey (45+4) pulled one back for the home team at Nehru Stadium at Fatorda here.
This was the second major title for Bengaluru FC in their two years of existence. They have won the I-League last season.
For Dempo FC, who won the title in 2004, they finished runners-up for the fifth time.
Bengaluru FC defender Curtis Osano was declared the Hero of the Match and was awarded Rs 10,000. Dempo's Romeo Fernandes, who scored four goals, was named Hero of the Tournament and earned Rs one lakh.
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But the complexion of the game changed after Bengaluru FC took the lead, which turned out to be the match-winner, in the 65th minute and then Dempo were reduced to 10 men three minutes later as defender Rowilson Rodrigues was shown a direct red card by referee Pratap Singh for a dangerous foul on Thoi Singh.
The match started at a slow pace but Bengaluru FC took the early lead as they earned a penalty after Dempo defender Haroon Fakhruddin pushed Eugenseson Lyngdoh down inside the box while going for an aerial ball from a flag kick taken on the left.
Dempo FC were unlucky not to earn a penalty midway in the first half as referee Pratap apparently did not see defender John Johnson elbowing Romeo Fernandes inside the Bengaluru box.