The Swiss opened the scoring in the 14th minute before debutant Tete Yengi equalised in the 56th at Snapdragon Stadium in San Diego on Saturday (Sunday AEST) in front of 6107 fans.
Like last week's 1-0 loss to Mexico, Switzerland were on top early, with Australia - albeit with a youthful line-up - only really settling after the drinks break in the 22nd minute and improving again after half-time substitutes.
That slow start will remain an area of concern ahead of next Saturday's Group D opener against Turkey in Vancouver, then matches against the United States and Paraguay.
"I'm just happy," coach Tony Popovic said.
"... Everything we wanted from the game we got. We got no injuries, we got a result that always helps, and we scored a very nice goal.
"So overall, we're happy. We need to start better, of course ... but we've got to try and manage those moments well when things aren't coming our way."
Irankunda, 20, started as a left-sided inverted winger and was by far Australia's most dangerous and explosive player while tracking back hard defensively before he was substituted in the 71st minute.
He was booked for kicking the ball at Granit Xhaka after the Swiss captain had been fouled.
Popovic felt Irankunda had found the first half difficult but grown into the game.
"We had three new front players, so that also didn't help him to understand clearly when to run forward, when to sit off, when to be in the pocket," Popovic said.
"But second half, like the team, he did better, and we know he's got those moments."
Debutant Cristian Volpato, newly defected from Italy, headlined a starting line-up which with an average age of 24.6 was the youngest team of the Tony Popovic era.
Volpato started as a right-sided attacker and grew into the first half, before being substituted at halftime.
Australia improved with the introduction of Connor Metcalfe and Jacob Italiano among others at halftime.
For Australia's goal, centre-back Cameron Burgess pulled off a scything long ball to brilliantly release Metcalfe, who squared the ball for a sliding Yengi to score.
Yengi also started among seven changes, with the immense and "outstanding" Harry Souttar captaining Australia for the first time and the impressive Patrick Beach in goal.
In the fourth minute, Irankunda forced a corner then whipped in a corner that Yengi glanced wide.
Beach denied Ndoye in the eighth and 12th minutes before Granit Xhaka sliced through the Australian defensive lines with a wonderful ball.
This time Ndoye trapped the ball then fire past Beach.
Australia found a foothold and in the 45th minute, Volpato curled in a wicked free kick to the back post and Souttar turned his header over the bar.
Four minutes into the second half, Irankunda won the ball with a powerful challenge, burst forward and let rip with a venomous strike that Gregor Kobel tipped onto the bar.
The Socceroos kept growing into the game and 10 minutes later, the well-deserved goal to Yengi arrived in a hurry.
Popovic emptied his bench and the Socceroos held on through a Swiss flurry.
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