Sporting high heels, a tight dress, butterfly eyelashes and a full beard, Wurst - whose birth name is Tom Neuwirth - swept to victory with her ballad Rise Like a Phoenix before a global TV audience of about 180 million people in 45 countries.
"I share the opinion that this was not a victory just for me but for the people who believe in a future that works without discrimination and is based on tolerance and respect. This transcends borders," said the 25-year-old "queen of Europe".
The UK's entry Molly Smitten-Downes only managed 17th place.
The Danish organisers of Eurovision had declared tolerance a main theme for this year's event