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.
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 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 onto the post on the half-hour mark, then denying Real Madrid star Arda Guler's dipping free kick in the 57th.
The 22-year-old denied Kerem Akturkoglu at point-blank range in the 78th, then batted away a free kick from captain Hakan Calhanoglu - who had said Turkey were more talented than Australia - in the 85th 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.
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.
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 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.
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