The vote had been fiercely opposed by Russia and Serbia, which attempted to get it postponed earlier in the day, Reuters wrote.
Russia's Foreign Minister Sergei Lavrov had warned on Friday against using UNESCO to legitimize what he called Kosovo's self-proclaimed state.
Kosovo declared independence from Serbia in 2008 almost a decade after NATO went to war to halt the killing and expulsion of ethnic Albanian civilians by Serbian forces trying to crush an insurgency.
Serbia does not recognize Kosovo as sovereign but signed up to an accord in 2013 designed to settle relations between the two as a condition of Belgrade's further progress towards membership of the EU.
The new country is so far recognized by 111 states, but not by Serbia or U.N. Security Council members Russia and China.
To win UNESCO membership, Kosovo needed a two-thirds majority. Of the 142 countries that voted, 92 backed the motion, 50 voted against and 29 abstained, meaning the bid fell short by three votes.
"The vast majority of the countries in the world have voted for Kosovo," Foreign Minister Hashim Thaci wrote on his Facebook page. "Unfortunately, for only three votes we did not win the needed absolute majority."
Kosovo is a member of the World Bank, the International Monetary Fund and the Olympic Committee, but has been struggling to join other international organizations due to Serbia's objections.
