The Islanders are now five points ahead of fifth placed Chennaiyin FC.
Mumbai City FC have kept two clean sheets in their last three home games and have registered two victories as well.
Diego Carlos scored the solitary goal of the game.
The versatile defender becomes second Indian player to move to Hyderabad FC in the January transfer window after Liston Colaco.
Odisha FC losing to FC Goa has given Mumbai City FC a great chance of moving up to the fourth spot.
Sougou has enjoyed a supreme run of form of late, scoring three goals in his last four games.
This was the first win for the Islanders in three games in the Indian Super League.