The 25-year-old was playing in his eighth match for his senior national side and, despite being a lethal scorer for Inter Milan at the club level, was still searching for his first goal for the Albiceleste.
He wouldn't have to wait long.
Inside the first two minutes Icardi had his side in front, taking down a long pass from Erik Lamela and cutting back on his left foot between two defenders before slotting home.
It was a brilliant first goal at the senior level and the Serie A star could hardly contain his excitement after the match.
"The goal was something I was missing," the 25-year-old told TyC Sports. "Luckily, it came through.
"I'm happy also. Excited. I was waiting for it. We talked about it a lot.
"For a forward, not scoring goals is an ugly thing. I hope I can continue like this."
Paulo Dybala also scored, his first international goal in 18 appearances, late in the match to seal another win for Lionel Scaloni, who has now picked up four wins in six without Lionel Messi since taking over as caretaker boss following the World Cup.
And Icardi believes there is a new spirit in the Argentina side, who have come together well under the 40-year-old interim manager.
"We all felt comfortable with everyone," he told reporters. "Something really good came together.
"I went through the last (cycle) and there wasn't as much spirit and friendship. Hopefully it continues.
"When I came here, I didn't feel that. I feel it now. We're all young. Before, with the experienced players, I didn't feel it.
"Now we're all starting from the bottom and we want to make a good impression on the coaching staff and our teammates. It's a plus. We all want the best."
Despite the developing friendships in the squad, the Inter star made it clear that Barcelona great Messi would be welcomed back with open arms as the team turns their attention toward their next major competition, the 2019 Copa America.
"Leo is the best in the world," he said. "The whole team wants (him back), to have a player like Messi.
“We're hoping he can be with us in the new year and we have him with us ahead of the Copa America."