Wednesday night's two FFA Cup quarter-final winners Wellington Phoenix and Melbourne Victory will face each other in the final four for the first time in the competition's history.

Embattled Wellington, who haven't won a major club trophy in almost two decades, edged past a COVID-ravaged Melbourne City side in a dramatic penalty shootout that ended 4-3 after regulation time finished 0-0.

Teenage Phoenix goalkeeper Alex Paulsen was the hero of the night, saving three spot kicks to help the New Zealand club qualify for the Cup semi-final for the first time.

They will take on an in-form Melbourne Victory team, who toppled two-time reigning FFA Cup winners Adelaide United 2-1.

Victory captain Josh Brillante, who scored on Wednesday, says an FFA Cup triumph can help restore the club's reputation as an A-League Men's powerhouse, having gone trophy-less since the 2018 A-League Men's grand final.

"I think everyone can see it and we can feel it," Brillante said.

"We've had a good start to the season and we've been able to get the results even though we're not playing some of the best football. It shows a winning team."

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Brillante and Victory won the Cup during Sydney FC's golden era under Graham Arnold in 2017; a win wedged in between two Sky Blue premierships.

"Cups are so important … it brings confidence through the season," he said.

"It's a piece of silverware. Any club wants to win that. And it's an Asian Champions League as well."

Brillante could end up facing his former club in the final if Sydney FC defeat Brisbane Roar in the postponed quarter-final, with the winner taking on Central Coast in the second semi.

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Reigning A-League Men's champions Melbourne City, meanwhile, continue to suffer the aftershocks of COVID-19, which has ravaged their playing squad.

City head coach Patrick Kisnorbo lamented the club's COVID situation following the Wellington loss, with all but five players catching the virus during the Christmas break.

"The boys showed great character, great resilience especially what they've been through," he said.

"We've overcome adversity and put on a good performance."

Brillante said Victory had "a few cases" among players in recent weeks.

"If you can avoid it, it's a good thing but I guess we're all going to be exposed at some stage," he said.

"So you're just going to do your best to stay safe and healthy and avoid it as much as you can.

"Everyone's doing the best they can and just preparing and hoping that games can go ahead."

AAP/ABC