Striker Robin Singh scored the game's only goal in the 68th minute.
The Red and Gold finished their group matches with seven points from three matches while Dempo stayed on three points from three matches.
The first half was marred by a flurry of missed chances and yellow cards – three for East Bengal and two for Dempo.
With both the teams going all out from the kick-off, the match was an entertaining one.
East Bengal made their first attempt in the 12th minute but Reisangmi Vashum’s long-ranger missed by a whisker. And almost immediately after, Dempo’s Ranti Martin failed to slot it in a Clifford Miranda cross.
After a barren first half, East Bengal scored the all-important goal in the 68th minute when Robin Singh, receiving a pass from Australian forward Tolgay Ozbey went past the rival goalkeeper to bulge the net.
Dempo’s best chance came in the 90th minute when they received an indirect free-kick inside the penalty box but couldn’t capitalise on it.