The Federation Cup champions led 1-0 at half-time with Chidi Edeh's 23rd minute strike on a hot and muggy afternoon at the Yubabharati Krirangan.
The Singapore league leaders found the equaliser through Shaiful Esah in the 69th minute.
But East Bengal had the last laugh when Lalrindika Ralte fired in the winner in the 87th minute.
The red-and-gold brigade remained on top position in Group H with 10 points from four matches to almost seal their last 16 knock-out berth.
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