Russia was able to muster only 10 other "no" votes - Armenia, Belarus, Bolivia, Cuba, North Korea, Nicaragua, Sudan, Syria, Venezuela and Zimbabwe.
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 it has 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 Deshchytsia told the assembly that his country's territorial integrity and unity had been "ruthlessly trampled" by Russia.
"This text is all about respect for territorial integrity and non-use of force to settle disputes," he said.
Russia's UN 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 UN Ambassador Yuriy Sergeyev countered in meetings with regional groups that Russia violated the UN Charter and stressed that the country is not a member of any bloc.
"The international community has sent a strong message through the passing of this resolution that Russia cannot simply trample over international law," British Foreign Secretary William Hague said in a statement after the vote.
US Ambassador Samantha Power, in urging a "yes" vote, stressed its call for a diplomatic, not a military solution, to the crisis and the need to de-escalate tensions and an electoral process that allows all Ukrainians to choose their leaders freely and without coercion.
"We have always said that Russia has legitimate interests in Ukraine," Power said. "It has been disheartening in the extreme to see Russia carry on as if Ukrainians have no legitimate interests in Crimea."
- AP