Joshimar da Silva Martins (43rd) and Gabriel Obatola (50th) scored for Salgaocar after Seiminlen Doungel had given Arrows a 36th minute lead.
Salgaocar now have 33 points to be on sixth place, while Pailan Arrows remained on 23, occupying 11th place in the standings.
Arrows started with Seiminlen Doungel in the attack while the other striker Holicharan Narzary was on the bench.
On the other hand, Salgaocar started with Joshimar and Gabriel upfront and their intent was clear from the word go.
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Salgaocar had another opportunity in the 28th minute when a Fulganco Cardozo shot deflected off Obatola's leg and came off the post.
Arrows took the lead when Seiminlen controlled a long ball from Vishal Kumar from the middle, dribbled past the Salgaocar defender Augustin Fernades before slotting the ball home.
Minutes later, Salgaocar got the equaliser when Joshimar headed home a Francis Fernandes cross from the right side.
Salgaocar got the winner when Obatola got the ball from the Arrows player Pritam Kotal, who failed to control a Joshimar header and released the former with the opportunity.
But Milan Singh attempt was not sharp enough to beat goalkeeper Karanjit Singh.