Veteran Dudu Omagbemi scored the winner in the 23rd minute and it was a one-way traffic for the Goans from there on as the wasteful Mohammedan Sporting disappointed their home fans at the Vivekananda Yuba Bharati Krirangan.
It was Mohammedan Sporting's (13 from 15) back-to-back losses after going down in Pune 0-2 as they find themselves in danger of relegation lying one point clear of bottom-rung Rangdajied United FC (12 from 16).
The Goans on the other hand brightened their hopes jumping to the fourth place with 24 points from 16 outings with their second successive wins after resuming the I-League.
Salgaocar had beaten Mohun Bagan by an identical scoreline in a home match to resume their I-League campaign.
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Mohammedan Sporting started out aggressively with Joshimar d'Silva Martins pressing forward as he was shown a yellow card in a 16th minute action.
Four minutes later, Syed Rahim Nabi latched on to a square pass from Israil Gurung but was unlucky as his angular volley hit the post.
Gurung wasted another chance in the first-half stoppage time when he fired a wayward long ranger after being fed by Penn Orji.
Second-half was nothing different for the hosts as this time Penn and Joshimar wasted chances to hand the Derick Perreira coached side full points.
In fact, the margin could have been more but Salgaocar were denied a penalty when Syed Rahim Nabi appeared to have handled the ball inside the box in the 77th minute but referee Pratap Singh thought otherwise.