Wurst was greeted at Vienna airport by hundreds of fans singing the winning ballad, "Rise like a Phoenix."
Wurst drew criticism from eastern Europe before Saturday's show, with some blasting her as an example of Western decadence.
However, Austria won points even from Russia. Wurst told a news conference shortly after her arrival in Vienna that shows "you can't reduce a country to its tolerance or intolerance."
"Yesterday was a victory not just for me, but also for those people who believe in future that functions without discrimination and which is based on tolerance and respect," Wurst said. "That was transnational and had nothing to with east and west."
President Heinz Fischer congratulated Wurst, the alter ego of 25-year-old Thomas Neuwirth — telling the Austria Press Agency it was "not just a victory for Austria, but above all for diversity and tolerance in Europe." Other political leaders joined in the congratulations.
Wurst told reporters that the victory doesn't put pressure on her because she doesn't consider herself "the ambassador of tolerance or the example" — though she is doing her "little bit."
"Shoot for the moon, even if you miss — you will land among the stars. That is exactly how I'm living," she said.
"I always say that my biggest goal is a Grammy, and on the way there I will grab everything that is given," Wurst added.
"Maybe I'll never get the Grammy. But maybe I will get things that are worth much, much more than any Grammy which could stand on my shelf. And that's why I will take everything I can get."
Geir Moulson contributed to this report from Berlin.