Toure grabbed a double while Irankunda snagged a stunning solo strike, and only a VAR intervention and a crossbar stopped the pair from adding two more goals on a banner night for Tony Popovic's youth-infused Socceroos.
Now the close friends from Adelaide hope that can be just the start of a brilliant attacking partnership.
"We train every day together in the off-season and then our first five seasons as professionals was together, and to do it for the national team as well has been amazing," Irankunda, 19, told Paramount Plus.
"We worked hard during the off-season for opportunities like this, chances like this.
"And I feel like tonight, we grabbed it with two hands, and we've shown the country and the world what we can do."
Toure, 21, added: "Now to see us both out here playing for the Socceroos is amazing.
"He's come a long way as a kid. He has a lot to learn - same with me. I'm also a kid. So we're both learning together."
Popovic's call to give Toure his first start alongside Irankunda was vindicated as the 21-year-old scored his double at Auckland's Go Media Stadium.
In the process, Toure laid down a marker to be Australia's starting striker going forward, and address the Socceroos' long-running, and often frustrating, hunt for a lethal No.9.
Toure struck a wonderful maiden international goal in the 35th minute, when Connor Metcalfe's teasing ball around Tyler Bindon was well met by the striker's splitting run between the centre-backs.
After beating Finn Surman for pace, Toure shrugged off Bindon before finishing with aplomb.
Watford winger Irankunda doubled Australia's lead with a stunning solo effort in the 54th minute.
Released on the right by Balard, Irankunda took off, beating Frances de Vries then jinking around Bindon, before finishing brilliantly across his body.
Star striker Chris Wood toe-poked home for New Zealand in the 57th minute after a missed Milos Degenek clearance.
But three minutes later, Irankunda found the excellent Metcalfe, who knocked the ball on for Toure to round Surman and score.
Toure was cruelly denied a maiden hat-trick when what looked like a third goal, off a superb combination with Lewis Miller, was chalked off for offside on the hour mark.
The match capped a marvellous window for Randers striker Toure, who assisted Max Balard's late winning goal in last week's 1-0 win in Canberra.
Australia claimed a 4-1 win on aggregate in the 'Soccer Ashes' and extended Popovic's unbeaten run in charge to 10 games.
Irankunda, in his first start since October, also clattered an extraordinary bullet of a long-range free kick off the crossbar in the 77th minute.
He quipped that he rated the shot "9.5 out of 10, because it didn't go in", believing it would have been the best goal of his career to date.
"When he shot, I almost died. I couldn't believe what's going on," Toure said.
"Like when he lined up, I said, 'Nestor, just don't embarrass us. Don't embarrass us.'
"And then he hits it, and it hits the crossbar. But that's Nestor for you - he does unexpected things."
Popovic, who also praised Irankunda for his work off the ball, said: "I'm in awe of that strike, really ... he's a special talent, a special shot that he has."
Midfielder Metcalfe was sensational, assisting both of Toure's goals.
Goalkeeper Paul Izzo was superb - including brilliantly batting away a bouncing Tim Payne header - before being substituted late on.
It was Australia's youngest starting team (average age 25 years and 331 days) in eight years, with 21-year-old defender Alessandro Circati named captain for the first time.
Circati was Australia's youngest captain since 1981.
