Karma Tsewang (eighth), Francis Fernandes (10th) and Clifton Dias (60th) saw Salgaocar take a commanding 3-0 lead.
Egged on by the local support, 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 in Kalyani 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.
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Even before the home team 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.