Darryl Duffy, who was drafted in the first XI for the first time, played a major role in Salgaocar's win as he hit the second goal and set up Douhou Pierre in the first goal.
Salgaocar, who led 2-0 at half time, scored through Pierre (43rd), Duffy (45th) and Brian Mascarenhas (65th).
East Bengal, who had large share of ball possession, pulled one back in the 77th minute through Dudu Omagbemi.
This victory, second in the league, takes Salgaocar FC to third place with eight points from five matches. East Bengal remained on seven points from four matches.
They preferred to guard their citadel and attack on counter with Duffy playing the lone striker upfront. He was instrumental in his team's victory.
The defense played an outstanding game in all four ties. Francis Kasonde kept Dudu Omagbemi and Ranti Martins quite and despite East Bengal doing most of the probing, they could not breach Salgaocar defence.
Abinash Ruidas, who spelled danger with couple of crosses, put Omagbemi clear inside the box but the willy striker saw his header go over the bar.
Two minutes later, Duffy received a pass from the left by Gilbert Oliveira and a firm shot found the roof of the net, beating goalkeeper Subhasish Roy Chowdhury.
After the change of ends, East Bengal defence once again fumbled and conceded another goal in the 65th minute.
Pierre stole the ball from Harmanjot Khabra, ran down the flank on the right and send a perfect cross into the box for Brian Mascarenhas, who beat the rival keeper with a left-footer, to score and take the game away from East Bengal.
