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The Mariners skipped out to a 2-0 lead in Tuesday night's match after first-half goals to Urena and Matt Simon.
But in a frenetic second half, Glory pulled one back in the 65th minute through Bruno Fornaroli, before launching wave after wave of attack in search of an equaliser.
Perth came close on numerous occasions, with Andy Keogh fluffing a header, Daniel Stynes having a close-range air swing, and Fornaroli sending a header just over.
Glory captain Diego Castro gave the Mariners all sorts of problems around the penalty area.
But the Mariners stood firm under the intense heat, with the win lifting them four points clear on top of the table.