The 22-year-old is expected to complete his move to Middlesbrough after his involvement at the tournament, with a deal agreed between Boro and Argentine side Banfield.
Payero was introduced in the 77th minute when Argentina were a goal down and chasing the game.
Mitchell Duke then scored Australia’s second goal to seal the contest, following Lachlan Wales’ 14th minute opener.
Argentina also had Francisco Ortega controversially sent off when the defender received two yellow cards before half-time.
The result leaves Argentina with work to do to qualify for the knock-out stages, ahead of a meeting with Egypt on Wednesday, July 25.
Their final Group C match is against a strong Spain side on Wednesday, July 28.
Boro boss Neil Warnock confirmed last week that a deal to sign Payero is close.
"I don't think all the financial details are finalised yet but as much as we can say,” said the Boro boss following his side’s 3-0 win over Bishop Auckland in a pre-season friendly.
"I had a good chat to the lad and he was looking forward to it. Nice lad and I think he's looking to build a platform for the next few years.
When asked where Payero could fit into the team, Warnock replied: "He can play eight and 10. He makes some good runs when he's further forward. He very rarely gives the ball away, good on set pieces.”
“He can chip in with goals as well.”