The all-important goal came in the 41st minute through Daryll Duffy.
Salgaocar, who looked better in the midfield, attacked on the flanks with Francis Fernandes and Gilbert Oliveira sending dangerous crosses that unsettled the rival defence.
Salgaocar central defender Chika Wali and Augustin kept a close watch on rival's playmaker Hugo Marchado, who did little precious in the middle which saw few raids from them and was latter replaced by Richard Costa.
Soon after Duffy again had a glorious chance to double the lead, but he headed wide off the target off Francis Fernandes cross from the right.
Churchill Brothers looked better in the second half after introduction of Micky Fernandes in place of Alesh Sawant, and rival keeper Karanjit Singh had to stretch himself on the right to put out a Lenny Rodrigues shot off Jaison Valles pass in the 62nd minute.