With more than half of the 35 million people living with HIV unaware they are infected, the battle is far from over however, said Michel Sidibe, head of UNAIDS.
"If we are smart and scale up fast by 2020, we'll be on track to end the epidemic by 2030, so that AIDS is no longer a public health threat," he told reporters.
"We have a fragile window of opportunity, because what we do over the next five years will determine the next 15."
That was the sharpest annual decline since the epidemic's peak in 2004 and 2005, and marked a 35-per cent drop from the 2.4 million deaths seen in both those years.
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New infections also fell to 2.1 million last year, down 38 per cent compared to the 3.4 million in 2001.
Africa remains the hardest-hit continent, with 1.1 million deaths in 2013, 1.5 million new infections, and 24.7 million people living with HIV.
Nine are in Africa: Cameroon, Kenya, Mozambique, Nigeria, South Africa, Tanzania, Uganda, Zambia and Zimbabwe.
But the spotlight is also on Brazil, China, India, Indonesia, Russia, and the United States -- where Black women, Hispanics and young gay man are most affected.
Globally, the report said 35 million people were living with the virus in 2013, up from 34.6 million the previous year.
A major problem, Sidibe said, is that 19 million do not know that they are HIV-positive.
To beat the disease, testing must be more widely available, given that tardy diagnosis is a key problem.
Discrimination is a key factor.
Nigeria criminalised homosexuality in January, and rights groups say people now fear seeking treatment, a test or mere information about HIV-AIDS, whether or not they are gay.
"People live in fear and this has an impact on HIV programmes," said Olumide Femi Makanjuola of the Nigerian group Initiative for Human Rights.
"Since the law passed, the number of people coming to our centre has reduced," he said.
In Russia, where injecting drug users and their sexual partners are the key group affected by AIDS, stigmatisation and a dearth of needle exchange and rehab programmes are a key problem.