Tony Popovic's Socceroos have one foot in the knockout stage after Irankunda, 20, became Australia's youngest World Cup goalscorer with a wonderful goal in the 27th minute, before Connor Metcalfe sealed victory with a glorious solo effort in the 75th minute.
The win on Saturday night (Sunday AEST) at Vancouver's BC Place sets up an enthralling clash with co-hosts the United States, who beat Paraguay 4-1 and lead Group D ahead of Australia, in Seattle on Friday.
"It's epic. It's unreal. Like, it's a dream come true," Irankunda told SBS.
"People underestimate us a lot, and we showed them today that we can play.
"They kept the ball a lot more, but who scored the goals?
"We scored the goals, and we showed them that we can play football."
It was the first time Australia have won their opening group stage match since 2006.
Popovic, who became the first Australian to play and coach at a World Cup, was rewarded for his bold calls to start Irankunda and pick Patrick Beach over captain Maty Ryan and Paul Okon-Engstler over Jackson Irvine.
Beach was wonderful, making a stunning fingertip save to turn Abdulkerim Bardakci's fierce strike on to the post on the half-hour mark, then denying Real Madrid star Arda Guler's dipping free kick in the 57th minute.
The 22-year-old denied Kerem Akturkoglu at point-blank range in the 78th minute, then batted away a free kick from captain Hakan Calhanoglu - who had said Turkey were more talented than Australia - in the 85th minute in front of 52,497 fans.
There were 10 World Cup debutants in the starting line-up, and an average age of 24.6, with captain on the night Harry Souttar the only player to have previously experienced the tournament.
But no one will be questioning Popovic now.
"It's something that we've always seen, and I've got a lot of belief in the young man," the coach said of Beach.
"He stood up today, so very happy for him.
"The young boys combining to score a goal - you can't underestimate what this will do for their confidence and belief."
The Socceroos weren't overwhelmed at the start, but took some time to work their way into the contest.
At the first drinks break, Popovic had an animated chat with Irankunda, then another with the entire group.
Minutes later, Beach quickly worked the ball to Cameron Burgess, who found Okon-Engstler.
The 21-year-old cleverly lofted the ball over the Turkey defensive lines for Irankunda, who with a brilliant first touch took out Merih Demiral, before finishing beautifully.
Irankunda ran to the corner flag and boxed it, in a tribute to the famous celebration of Socceroos great Tim Cahill - his idol growing up.
"Tim Cahill, Australia's greatest in my opinion, and I just thought if I scored, I'll do the same as him," Irankunda said.
Turkey called on Juventus star Kenan Yildiz at halftime in a bid to turn the tide.
Souttar had a header batted away by Cakir in the 54th minute, but between Beach's heroics Metcalfe went on an incredible weaving run before skidding an unstoppable shot inside the near post.
Australia's brilliantly desperate defence would not be bested from there, despite a late Turkey barrage.
8°C