Australia boss Ange Postecoglou described Tim Cahill as "a unique and extraordinary individual" and also "a freak" after his two goals sealed their place in an intercontinental World Cup play-off.
The former Everton star was handed a starting spot in Tuesday's second leg of the AFC play-off against Syria and repaid his coach's faith with both goals in their 2-1 extra-time victory.
Cahill cancelled out Omar Al Soma's shock opener before heading in a 109th-minute winner to secure a 3-2 aggregate victory and become the first player to reach 50 international goals for the Socceroos.
Postecoglou says the 37-year-old is undoubtedly the country's best player in history and was amazed with the way he performed over 120 difficult minutes against a stubborn Syria side, who almost snatched an away-goals victory in the dying seconds through an Al Soma free-kick that hit the post.
"Timmy was Timmy and that's simply why he's the greatest ever," Postecoglou said.
"He's just a freak. I'd hazard to think when the last time he played 90 minutes was, let alone 120.
"He's just got real belief in himself, a real unique and extraordinary individual and he led from the front today.
"I think Timmy would've belted me if I took him off. We haven't flogged him; we've used him when we needed to."
Cahill believes he had the defenders worried from the outset and was delighted to defy critics who worry he is too old for international football.
"When I play, I know the defenders are going to be scared, not because I'm Tim Cahill but because of my presence and what I give," said the Melbourne City man, who will turn 38 in December.
"I'll run to the end for these players and this manager. In the end, you get your reward.
"I'm proving that being professional as long as you can and respecting the game — you get the rewards."
Australia will go into a play-off next month against the fourth-place team in the final CONCACAF standings, which will be either the United States, Panama or Honduras.