Salgaocar, who led 2-1 at half time, scored through Thongkhosiem Haokip (4th, 90+2) and Cavin Mbarga (36th) to register their first win at home here.
East Bengal, who fought back strongly in the second half, reduced the margin through Ranti Martins (25th minute).
Salgaocar now have 8 points from 10 matches, while East Bengal remained on third place with 17 points from 9 matches.
Salgaocar, who went down 1-3 to Mohun Bagan, were desperate to win and started well with Darryl Duffy and Haokip working in tandem to put early pressure on the rival defense and they succeded in finding an early goal in the 4th minute.
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East Bengal retailated and almost equalised four minutes latter when Ranti Martins ran down the left flank off a pass from Sanju Pradhan and on entering the box took a shot at the goal which missed the target narrowly.
Salgaocar received an early blow when their reliable striker Duffy got injured and was replaced by Jackichand Singh and they had a close shave in the 16th minute when defender Eder made a goal line save off Jairu's shot after keeper Karanjit Singh was beaten by Samad Al Mallick's cross.
Thereafter, it was an even contest as both the teams tried to take the lead and Salgaocar earned a penalty and once again took the lead in the 36th minute.
Jackichand Singh, who troubled the defense with his speedy run, outmarted Mallick inside the box and the East Bengal's defender pulled him down and referee had no hesitation in awarding the penaty spot which Cavin Mbarga converted to have Salgaocar leading 2-1 at half time.
East Bengal were reduced to ten man in the 78th minute when defender Sehnaj Singh got the marching orders from referee Umesh Bora for a rash tackle on Jackichand. This helped the home team as Haokip scored his brace in the injury time to seal the issue for Salgaocar.