Perth edged Sydney FC 1-0 as Sydney captain and former Juventus Alessandro Del Piero came back from a hamstring injury in the 62nd minute but couldn't equalize for the visitors.
Sydney lost on what appeared to be a missed offside call and an ensuing penalty.
Glory forward Ryo Nagai appeared to be offside attempting to run onto a good pass from Jamie MacLaren which would have left him one-on-one with Sydney goalkeeper Vedran Janjetovic. When the offside call wasn't given, Janjetovic ran into the back of Nagai and caught him high, clearly a penalty call.
Steve McGarry slotted home the penalty in the ninth minute for the only goal of the match.
Sydney FC coach Frank Farina was left frustrated at the missed offside call and his team's lack of scoring touch. His side has just three points from four matches and has scored just two goals while allowing seven.
"We created chances which we didn't take, and you pay for that," Farina said. "In terms of the way we played, I thought we did very well. I thought we were by far the better side."
On Monday, former Millwall captain and Australia international Kevin Muscat will coach the Melbourne Victory for the first time when they host Wellington to conclude the fourth round.