In the non-binding vote in the General Assembly in New York, 116 states were in favour and only six against, a major diplomatic blow to the UK.
Fifty-six states, including France and Germany, abstained.
Mauritius says it was forced to give up the Indian Ocean group - now a British overseas territory - in 1965 in exchange for independence.
In a statement to the BBC, the UK's Foreign Office said Britain did not recognise Mauritius' claim to sovereignty, but would stand by an earlier commitment to hand over control of the islands to Mauritius when they were no longer needed for defence purposes.
After the UK took control of the islands, it evicted the entire population and operates a joint military base with the US on Diego Garcia, one of its larger atolls.
The latest vote comes months after the UN's high court advised that the UK should leave the islands "as rapidly as possible".
Mauritian Prime Minister Pravid Kumar Jug-Nauth told the General Assembly the forcible eviction of Chagossians was akin to a crime against humanity.
Before the vote, Mr Jug-Nauth said UN members must send "a clear signal to the world that colonialism can no longer be tolerated".
The UK has maintained that Mauritius gave up the territory freely in return for a range of benefits.
Its UN Ambassador, Karen Pierce, called Mr Jug-Nauth's statement a gross mischaracterisation, adding that it should be resolved only by the countries involved.