The US ambassador to the UN, Samantha Power, said the historic decision reflected the new policy of engagement over isolation.
Diplomatic ties with Cuba were restored in 2015, but Republican-controlled Congress opposes lifting the longstanding embargo.
The vote passed overwhelmingly, with the support of 191 countries.
Only Israel abstained alongside the US.
The UN General Assembly has voted to approve the resolution every year since 1992, and the US has always strongly opposed it.
“After 55-plus years of pursuing the path of isolation, we are choosing to take the path of engagement,” Samantha Power said.
She added, however, that the abstention did “not mean that the United States agrees with all of the policies and practices of the Cuban government”, including “serious human rights violations”.
The decision at the UN General Assembly led to immediate protest from US politicians opposed to lifting the embargo.
Texas Republican Senator Ted Cruz tweeted that the act imposing sanctions on Cuba was “the law of the United States, which should always be defended and upheld”.
Cuban Foreign Minister Bruno Rodriguez said Cuba was “grateful” for Samantha Power’s efforts.
“A change in vote by the United States is a promising signal,” he said.
“We hope it will be reflected in reality.”
While UN resolutions of this type are non-binding and non-enforceable, the annual resolution has for 25 years allowed Cuba to demonstrate that global opinion is against America’s Cuba policy.
Cuba says the embargo prevents sick people from being treated with much-needed US medical equipment and farmers from modernizing their agricultural methods.
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