The triumph lifted Victory into second spot on the table, giving them a one-point buffer over third-placed Western Sydney with just four rounds remaining.
Perth Glory remain bottom of the table after their winless run stretched to nine games.
The Victory, who were playing their third game in the space of nine days, now have to back up for Tuesday’s Asian Champions League clash with Japanese outfit Yokohama F. Marinos in Melbourne.
There was drama during the warm-up when Glory young gun Danny De Silva was knocked unconscious after being struck in the side of the head by a wayward ball.
De Silva was replaced on the bench by Adrian Zahra, and Glory took a surprise lead in the 27th minute when Michael Thwaite’s header deflected off Milligan and into the back of the net.
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Glory goalkeeper Jack Duncan pulled off a brilliant fingertip save to deny Tom Rogic three minutes later.
But Victory were back on level terms before half-time when Milligan converted a penalty after Troisi was pulled down by Glory defender Matt Davies.
Clear-cut chances on goal were few and far between in the second half.
But Thompson made no mistake when a golden opportunity finally fell his way, with the fringe Socceroo slicing his way behind Glory’s defence before nailing the late winner in front of 7068 fans.