Mariners goalkeeper Liam Reddy was beaten in the 42nd minute when Marinkovic found the top-right corner with a wonderful curling strike from a set-piece.
The hosts were unable to respond, despite dominating possession, as they suffered a third consecutive defeat and the Glory picked up a first regular-season win at Gosford.
Perth were forced to survive a couple of scares in the second half, with Mitch Duke forcing Danny Vukovic into a sharp save and substitute Malick Mane going close in the dying stages.
Duke had also spurned his side's best opportunity prior to Marinkovic's goal, after pouncing on a loose ball in the Glory box.
However, Kenny Lowe's side were able to keep a clean sheet and now hold a one-point lead over Melbourne Victory, Sydney and Adelaide United at the top of the table.
