REYKJAVIK—Voters here blew a loud raspberry at Iceland's political establishment Saturday, handing victory in the capital's municipal elections to an upstart political party that ran a blatantly satirical, humor-based campaign.

After promising a polar bear for the Reykjavik zoo and making other unorthodox proposals, the six-month-old Best Party won 34.7% of the vote, securing six of the 15 seats on the city council. It was closely followed by the Independent Party—the traditional powerhouse in the city—with...