The vote on the Ukraine-sponsored resolution was 100 countries in favor, 11 opposed and 58 abstentions.
The "yes" vote was higher than many diplomats had predicted, and the fact that more than half the 193 U.N. member states supported the resolution reflected widespread international opposition to Russia's military intervention and takeover of the strategic Black Sea region.
Unlike the more powerful Security Council, resolutions in the General Assembly cannot be vetoed but are not legally binding.
Russia has blocked action in the Security Council where they have veto power as one its five permanent members. Even so, the 15-member council has held eight meetings on Ukraine, as Western powers strive to keep up the pressure on Moscow.
Before the vote, Ukraine's Foreign Minister Andriy Deshchytsia told the assembly that his country's territorial integrity and unity had been "ruthlessly trampled" by Russia, a permanent member of the Security Council entrusted to maintain international peace and security, and in direct violation of the U.N. Charter.
"By voting in favor of this resolution you vote in favor of the U.N. Charter while voting against or abstaining equals undermining it," Deshchytsia said in urging a "yes" vote.
Russia's U.N. Ambassador Vitaly Churkin urged a "no" vote, saying a historic injustice in Crimea has been corrected and its people had expressed their right to self-determination in wanting to join Russia.
He called the resolution "confrontational in nature" and said it would be "counterproductive" to challenge the results of the referendum.
Over the past week, Churkin mounted a campaign against the resolution, claiming the dispute is an East-West issue. Ukraine's U.N. Ambassador Yuriy Sergeyev countered in meetings with regional groups that Russia violated the U.N. Charter and stressed that the country is not a member of any bloc.
Crimea has been at the center of Europe's greatest geopolitical crisis since the end of the Cold War. Russian troops took over the Ukrainian peninsula, where Russia's Black Sea fleet is based, and Moscow officially annexed Crimea following a referendum last week.
The upheaval in Crimea is the fallout of months of anti-government protests and outbursts of violence that led to the ouster of Ukraine's pro-Russia president, Viktor Yanukovych, who fled last month.
The resolution adopted Thursday says the referendum on Crimea has "no validity" and calls on all countries and organizations not to recognize Russia's annexation.
It also calls on all parties to immediately pursue a peaceful resolution of the situation in Ukraine "through direct political dialogue."
Associated Press writer Cara Anna contributed to this report.
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