Popovic had handed starts to Melbourne City goalkeeper Patrick Beach ahead of captain Mathew Ryan, and played A-League product Paul Okon-Engstler in the side.
Both calls were vindicated inside the opening half hour.
Okon-Engstler's pass sent Irankunda clear, and the 20-year-old finished coolly into the bottom corner in the 27th minute to break the deadlock.
Metcalfe doubled the advantage in the 75th minute, driving a low strike into the bottom corner from the edge of the box to leave Türkiye, appearing at their first World Cup in 24 years, with work to do in their remaining group fixtures.
Speaking after the final whistle, Popovic reflected on the emotional weight of the occasion.
"Proud. Proud to be here as head coach. To experience this, put a smile on people's faces who have travelled so far to support us and just happy for a group of wonderful young men."
He extended that praise to his coaching staff.
"Just proud of the staff and the work they put in. Some good decisions on the sideline. Tried to guide them, tried to support them."
Asked about Beach's performance, which included a string of saves to deny Türkiye's Arda Güler and Abdulkerim Bardakci, Popovic backed his goalkeeping call.
"It's something that we've always seen and I've got a lot of belief in the young man. He stood up today and I'm happy for him."
On the combination that produced the opening goal, involving two of his more unconventional picks, Popovic highlighted the wider impact for the squad.
"That was quite special seeing the young boys combine for the goal. You can't underestimate what this will do for the confidence and belief. Emotionally, it will give a lot to the players from this game. We can give back and recover well and focus on the US."
Popovic also praised Metcalfe, the FC St. Pauli midfielder whose Bundesliga form had earned him a recall to the squad.
"He's probably the fittest that he's been with us, he got a couple of games with St Pauli before he arrived into camp and you can see the benefit of that. He's put in a lot of work and I'm happy he got a goal. We keep asking him to shoot more and he should do better with his left foot. It's perfect he should score."
Irankunda, whose finish set Australia on their way, described the moment as the realisation of a long-held ambition.
"It is unreal. A dream come true. We've got the win right now. We worked extra hard, we thought until the end. It's an exciting moment."
The forward also reflected on becoming Australia's youngest World Cup goalscorer.
"It feels amazing. You've got to thank the staff, you've got to thank the nation. They all believe in me to do so well and today, getting that goal was amazing. It is just a great feeling."
Australia now sit on three points alongside the United States at the top of Group D, with their performances against Türkiye offering early evidence that Popovic's faith in youth could carry the Socceroos deep into the tournament.