The power ballad, "Rise Like a Phoenix," helped Wurst — the alter ego of 25-year-old Thomas Neuwirth — secure Austria's second victory in the competition with 290 points. The country also won in 1966.
"This is dedicated to everyone who believes in a future of peace and freedom," a tearful Wurst said as she accepted the trophy from Denmark's Emmelie de Forrest, who won the contest last year. "We are unity."
Pushing the boundaries of gender identity is nothing new at Europe's annual song contest, an extravaganza known for its eclectic, sometimes unlistenable lineup of techno beats, love songs and pop tunes. The winner in 1998 was Israel's Dana International, who had male-to-female gender reassignment surgery several years before competing.
Still, Wurst had been faced with some protests before the competition, highlighting a rift between Europe's progressive liberal side and the traditional values and nationalist rhetoric of Russia and some other nations taking part.
Amid growing tensions over the Ukraine crisis, some in Eastern Europe have blasted Wurst as an example of the West's decadence. Activists in Belarus had even urged the country's state television network to bypass the live broadcasting rules by the organizers and edit the Austrian entry out of its Eurovision transmission.
After her victory, Wurst told reporters she hopes gay, lesbian, bi and transgender people around the world are getting stronger in their fight for human rights.
Asked if she had anything to say to Russian President Vladimir Putin, who introduced a law last year prohibiting so-called gay "propaganda," Wurst said, "I don't know if he is watching this now, but if so, I'll say it: 'We're unstoppable.'"
In Vienna, the Austrian capital, fans who had gathered at one of the public viewing parties chanted "Conchita" ecstatically after the victory. Some had painted on fake beards in support.
Neuwirth, who was born in Gmunden, central Austria, entered show business eight years ago, taking part in an Austrian TV talent show. After joining a boy band that quickly broke up, Neuwirth first appeared as Wurst in another Austrian talent show in 2011. She also took part in two reality shows, including one where candidates had to survive in the Namibian desert together with native tribes.
Juries and television viewers across Europe selected her as the winner ahead of The Common Linnets from the Netherlands with 238 points and Swedish singer Sanna Nielsen with 218, meaning next year's contest will be held in Austria.
Other notable entries included Polish group Donatan & Cleo's semi-pornographic show featuring women in low-cut milkmaid outfits and Montenegro's Sergej Cetkovic, who had a faux-ice skater circling around onstage.
The annual competition is supposed to be completely removed from politics. Neither Russia's entry — teenage twins Anastasia and Maria Tolmachevy — nor Ukraine's Mariya Yaremchuk, whose routine included a dancer running in a giant hamster wheel, alluded to the recent tensions between Moscow and Kiev.
Still, every time Russia got votes many in the audience of 10,000 booed, and when Moscow gave its respective eight, 10 and 12 points to Armenia, Azerbaijan and Belarus — all former Soviet republics — more boos were heard.
Many former Soviet republic countries gave their points to neighboring countries, except Ukraine, whose eight points to Austria were decisive for the Danish hosts to declare Wurst had won.
The first Eurovision song contest was held in 1956 in Switzerland, and the contest's most famous winners include ABBA, Celine Dion and Johnny Logan, who won the contest three times — in 1980 and 1987 as a performer, and in 1992 as a songwriter.