Perth were completely dominant in the first half, with 37-year-old Diego Castro serving up a masterclass in midfield in his 100th A League game.
The Phoenix had more chances in the second half, and introduced former Celtic and Norwich City striker Gary Hooper late in the match, but Perth were content to sit on their lead, though Davila notched a late consolation from the penalty spot.
In difficult windy conditions, the Phoenix made a promising start, looking to play an up-tempo game.
But the experienced Perth team, one of the oldest in the A-League, soaked up the pressure before taking a chokehold on the game.
They opened the scoring through Bruno Fornaroli, who showed quick feet and even quicker thinking to dink the ball inside the near post in the 11th minute.
It was clever, but also highly preventable.
Castro was allowed to roam down the left, despite the presence of two Phoenix players, and his cross found Fornaroli, who was given too much space on the edge of the six yard box.
From there Perth raised the stakes.
Kim Soo-Beom were denied from 12 yards by Stefan Marinovic, before the All Whites keeper twisted his body brilliantly to keep out a close range Fornaroli header.
Perth defender Gregory Wuthrich was lucky to escape with a caution midway through the first half, after a crude two footed tackle from behind on David Ball, the kind of challenge that 1980s Italian enforcer Claudio Gentile would have been proud of.
Wellington tried to play a possession game, through the lines, but their forwards were left mainly chasing hopeful balls, and visitors went further ahead in the 33rd minute.
Chris Ikonomidis finished with aplomb, after Fornaroli latched onto a lofted Castro pass, but again the Wellington defending was passive and the marking loose.
Wellington's best first half chance fell to Davila, after nice interplay with Callum McCowatt, but the Mexican dragged his shot just wide of the far post.
Perth should have had a third on the stroke of halftime, but for a remarkable piece of defending by Louis Fenton, who dived in front of Fornaroli to prevent the South American from heading home.
The second half was a scrappier affair in the blustery conditions, with yellow cards and stoppages, which suited Perth and frustrated Wellington.
Jaushua Sotirio had a good opportunity, but looped his header way over the bar, while Ball poked a near post effort wide.
Davila and McCowatt also forced saves from Liam Reddy, but Perth were relatively comfortable, before Davila's 95th minute penalty, after Hooper was bundled over in the box.
Perth Glory 2 (Bruno Fornaroli, Chris Ikonomidis goals)
Wellington Phoenix 1 (Ulises Davila pen)
Halftime: 2-0
