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Sung in Ukrainian, the winning song fused rap with traditional folk music and was a tribute to band frontman Oleh Psiuk's mother.
The bookmakers had made Kalush Orchestra the clear favourite for the annual contest, which normally draws a television audience of close to 200 million, based in part on popular sympathy for Ukraine following Russia's invasion in February.
Ukrainian President Volodymyr Zelenskiy was quick to offer his congratulations.
"Our courage impresses the world, our music conquers Europe! Next year Ukraine will host the Eurovision song contest," he said in an online message. The winners traditionally get to host the event the following year.
"I thank the Kalush Orchestra for this victory and everyone who gave us your votes! I am sure that the sound of victory in the battle with the enemy is not far off," he added.
Ukraine were in fourth place based on jury voting but claimed victory with a commanding lead in viewer voting. Britain's Sam Ryder finished second, while Chanel of Spain finished third.
It is the third time that Ukraine has won the annual competition.
The band's frontman made a plea for the city of Mariupol and its Azovstal plant at the end of their appearance.
"Please help Ukraine, Mariupol. Help Azovstal right now," Psiuk shouted from the front of the stage.
The European Broadcasting Union, which organises the contest, said no action would be taken against the band for using the stage to make a statement.
"We understand the deep feelings around Ukraine at this moment and believe the comments of the Kalush Orchestra and other artists expressing support for the Ukrainian people to be humanitarian rather than political in nature," the EBU said in a statement.