It was a sloppy display for the home side with Edeh Chidi missing a penalty while the team was reduced to 10 players after Uga Okpara was sent off following a double yellow in the 75th minute.
Dempo, on the other hand, were all guns blazing with a brace from Beto (54th and 76th) and captain Clifford Miranda who gave the Goans a third minute lead as they logged their first three points in the fifth round fixture at Kalyani Stadium.
Dempo now have six points from five matches, while East Bengal who had a delayed start to their I-League campaign remained on three from two matches.
East Bengal were caught unaware as early as in the third minute when Billy Mehmet's low cross from the right was well executed by Miranda putting it past Abhijit Mondal who was picked ahead of Gurpreet Singh Sandhu.
Keen for a big win ahead of their home and last leg semi-clash against Kuwait SC in the AFC Cup on October 22, Marcos Falopa put up their full strength side but the intent was missing.
The red and gold brigade got back to back chances in the 20th minute but James Moga and Chidi let the home fans down.
But the biggest blow to the home camp came in the 35th minute when Chidi missed to score from the spot with a shoddy shot that went wide off the left post as Dempo held on to their slender lead.
Dempo doubled the lead when Miranda swung in a corner which beat the home team defenders and goalkeeper Mondal who missed an easy catch allowing Beto to fire in at the far post.