Needing a win to snatch the title ahead of other established teams, Bengaluru led from start to finish.
They scored through Sean Rooney (2nd), Robin Singh (56th), John Menyongar (79th) and captain Sunil Chhetri (90+7).
Dempo reduced the margin through Roberto Silva (82nd) and substitute Romeo Fernandes (89th).
After Sean Rooney had given them a dream start in the second minute, there was no looking back. Dempo threatened a brief fightback but that was not enough to thwart Bengaluru.
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Bengaluru needed a win from any of their last two matches to emerge triumphant but in the end it was clear that they would not leave anything to chance.
Robin Singh scored in the 56th minute to give his team a 2-0 lead. With ten minutes left to be played, Bengaluru put the issue beyond doubt when John Menyongar made it 3-0.
But India and Bengaluru captain Sunil Chhetri scored the winners' fourth goal of the evening.
Coach Ashley Westwood was suspended for the game and assistant coach Pradyum Reddy took charge in the dugout. But Westwood had done enough in pre-match preparations to help his team sail through.
They started with a flourish when Rooney gave them a second-minute lead.
Captain Chhetri took a quick throw in to Robin, whose shot across the goal was met with glee by Rooney past a bewildered Dempo defence.