The body, which regulates trade in flora and fauna, voted by a two-thirds majority to upgrade the sharks' status.
Campaigners hailed the move as historic and said the vote represented a major breakthrough for marine conservation.
The decisions can still be overturned by a vote on the final day of this meeting later this week.
The oceanic whitetip, three varieties of hammerheads and the porbeagle are all said to be seriously threatened by overfishing.
Their numbers have declined dramatically in recent years, as the trade in shark fins for soup has grown.
Manta rays are killed for their gill plates which are used in Chinese medicine.
Shark supporters have been attempting to get Cites to protect these species since 1994. But there has long been strong opposition to the move from China and Japan.
But a number of factors have changed the arithmetic.
Experts say the critical factor has been a shift in South American nations, who've come to understand that sharks are more valuable alive than dead.
"They've come to realise, particularly for those with hammerhead stocks, the tourist value of these species and the long term future that will be protected by a Cites listing," said Dr Colman O'Criodain from WWF International.Regulate, not ban
While the vote to upgrade these shark species to Appendix 2 does not ban the trade, it regulates it. Both exporting and importing countries must issue licences. If a nation takes too many of these species, they can be hit with sanctions on the range of animal and plant products that are governed by Cites.
As the votes went on there were smatterings of applause in the hall and some high fives among campaigners.
"It is really significant for Cites to come of age like this," Dr Susan Lieberman told BBC News.
"To say we can deal with these species, we can manage the international trade and lets not be afraid of marine species."
The extension of the authority of Cites into the international trade in fish has long worried China and Japan and the Asian nations were strongly against these proposals.
But many West African countries, who have seen their native shark fisheries destroyed by large offshore operations, voted in favour of the restrictions.
Another factor was money. Especially cash from the European Union.
The head of delegation told the meeting that extra money would be made available to help poorer countries change their fishing practices.
"If there's a need for it the funding will be available," Feargal O'Coigligh told the meeting.
The amendments can still be overturned in the final session of this meeting. And this realisation is tempering the celebrations.
"Cites is ready to come of age for marine species, " said Dr O'Criodain.
"As long as we hold these results in plenary. Maybe warm champagne is the right note."
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