The 25-year-old performer, whose real name is Tom Neuwirth, took the Eurovision crown in Copenhagen despite initial expectations that the eye-catching performance would be too controversial in socially conservative countries.
"We are unity, and we are unstoppable," she said after winning the glitzy competition with 290 points compared with 238 points for runner-up the Netherlands, in what Eurovision fans had anticipated would be a more closely fought race.
Austria's Wurst didn't become one of the bookies' top candidates until Thursday's semi-final, amid reports that the drag act had prompted shocked petitions in Russia, Ukraine and Belarus.
Even in Austria, the leader of the right-wing FPOe party had called the act "ridiculous".
"I have very thick skin. It never ceases to amaze me just how much fuss is made over a little facial hair," Wurst told AFP on Friday.
The Eurovision winner, who was visibly overcome by emotion after accepting the prize, secured most of her "douze points" from western European countries including Britain, Sweden and the Netherlands.