Liverpool were finding opportunities harder to come by compared to their clash against a Thailand All-Star side earlier this week, with clear-cut chances proving to be few and far between in the opening throes.
The home side, currently sixth in the A-League ladder, then upped the pressure as the first half wore on and they were duly rewarded 17 minutes in when Dimitri Petratos found a way through.
After being picked out in space on the edge of the box, the attacking midfielder managed to slot the ball beyond the reach of Mignolet to open the scoring.
Liverpool had an instant chance to respond through Danny Ings, who was unable to make the most of fellow new boy Joe Gomez's cross into the box, while only a fine stop from Jamie Young kept out the former Burnley man soon after.
Petratos and Brandon Borrello both saw chances come and go before the half was out, but it was the visitors who came closest to finding the game's third goal when Sakho's header was cleared away off the line.