Left-back Traore lashed home a vicious drive from long range in the 36th minute, one of the few highlights in a lacklustre contest, with substitute Finkler sealing the points with a minute remaining.
Victory's first win in three games sees them climb to third place in the A-League ahead of the rest of this weekend's Round 10 action, while Perth remain seventh in the table and winless on the road in 2013-14.
For anyone who has seen Victory dominate possession but fail to make their chances count on numerous occasions this season, there would have been a strong sense of deja vu in the first half in Melbourne.
The home team controlled the play and were largely camped out in Perth's defensive third, but they were restricted to long-range shots from the likes of Mitch Nichols, Kosta Barbarouses and James Troisi, which rarely troubled Glory goalkeeper Danny Vukovic.
It looked very much as if another night of frustration might be in store, but nine minutes before half-time Nichols laid the ball back for advancing fullback Traore, who took one touch before lashing a dipping strike from outside the area past Vukovic at his near post.
The Glory wasted their best chance of the match in the 80th minute, when Ryan Edwards shot over the crossbar after seizing on a loose ball unmarked in the centre of the penalty box.
But any slim hopes Perth harboured of earning a share of the spoils were crushed in the 89th minute when Finkler was played in on goal by the quick feet of Troisi, the Brazilian dispatching a low shot past Vukovic to cap off a lively cameo.
In a side-plot to the game sure to concern the Victory board and administration, the club's rebellious 'North Terrace Collective' left the match at half-time to demonstrate outside against perceived ill treatment at the hands of authorities, negotiations with the club over contentious security measures having broken down in the days leading up the game.
The absence of the Victory's largest active supporter group made for a distinctly low-key atmosphere at what was previously one of the A-League's loudest venues.
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