Karma Tsewang (eighth), Francis Fernandes (10th) and Clifton Dias (60th) gave Salgaocar a commanding 3-0 lead before East Bengal recovered some of the lost ground.
Egged on by the local crowd, East Bengal had a late surge with two goals from James Moga (64th) and substitute Semilen Doungel (77th) but it was not enough as the Goans emerged winner in the five-goal thriller.
The win was more important for Salgaocar as it was their first ever away win over East Bengal in the I-League.
Having beaten United SC 2-0 here in round seven, Salgaocar were confident of another positive away result as Karma scored past East Bengal custodian Abhijit Mondal after Naoba Singh had cleared Darryl Duffy's initial effort.
Even before East Bengal could recover from the jolt, India international Francis made it 2-0 just two minutes later. The wide midfielder chipped the ball over an onrushing Abhijit after a brilliant solo run as the visitors doubled their advantage.