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A first-half strike from Joel Chianese was enough to settle the contest, and despite intense pressure and firing off 32 shots to Perth's 15, the Phoenix were unable to find an equaliser and have exited the finals series at the first time of asking.
On another day, one of Wellington's plethora of chances would have found its way into Glory's net, but a combination of well-organised defending, excellent goalkeeping and a fair amount of fortune saw Perth hold their lead and advance at the Phoenix's expense.
The Phoenix will be left to rue their inability to finish their opportunities, and nine weeks after jetting out of New Zealand's capital to continue the A-League season in New South Wales, their Australian adventure ended in anything but the fashion they had hoped for.
"Football's a cruel game sometimes," coach Ufuk Talay said.
"You dominate a game, create enough opportunities to win and it's a recurring theme from the last game against Newcastle. If we're not clinical in front of goal, we can't win games. We create, but we're just not clinical.
"We gave them one opportunity where they scored and then I think we totally dominated the game but we didn't score a goal to get ourselves back into it."
The game's only goal came after 18 minutes when Chianese, who had scored twice for Sydney FC in a finals match against Wellington eight years ago, latched on to a neat through ball from Jake Brimmer, sped between two defenders and produced a tidy left-footed finish to beat Phoenix goalkeeper Stefan Marinovic from 15 yards.
Going behind was the catalyst for an increased first-half intensity from the Phoenix, who won a raft of set pieces and eventually attempted 17 shots before the break without opening their account.
In particular, two goal-bound efforts from Ulises Davila were brilliantly saved by Liam Reddy, who 10 years ago was the penalty shootout hero as the Phoenix beat the Glory in their first finals match. A decade on, and now with Glory, he was a formidable final barrier in the path of his former side.
As the second half wore on, Wellington's attack became more and more desperate. Reno Piscopo flashed a right-footed effort just wide of the post, Steven Taylor was unable to direct a volley on target from a narrow angle and the outstanding Libby Cacace – in what will be his last game for the club – becoming increasingly more prominent, driving deep into enemy territory time and again to set up chances which went unconverted.
As the game entered its final quarter, Jaushua Sotirio spurned a chance from a handy position after a run and cross from fullback Callan Elliot. There was also a suggestion of a Phoenix penalty when Tomislav Mrcela's high foot seemed to make contact with substitute Callum McCowatt, but referee Alex King saw nothing untoward. As time ticked down, David Ball's swivel-volley cannoned off the crossbar.
"I'm still very proud of the boys," Talay said.
"I think this is a great experience for our younger players playing these games. The more they play in these finals series, the more accustomed they get to it and the better experience they get from it."
The win sees Glory advance to face Sydney FC in the second semifinal on Wednesday night. Melbourne City will meet the winner of tomorrow night's second elimination final between Brisbane Roar and Western United.
Despite his first season as a head coach ending in this fashion, Talay said he still regarded the campaign as a success.
"I've thoroughly enjoyed it."
"We've got a great bunch of boys. We started off on the back foot but the belief and the process was there and it got us to third on the table.
"That's our template and we'll build on that hopefully for next season."
Perth Glory 1 (Chianese 18'), Wellington Phoenix 0.