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."
In a report released ahead of the 20th International AIDS Conference in Australia from July 20-25, the UN agency said AIDS-related deaths dropped to 1.5 million in 2013 from 1.7 million the previous year.
That was the sharpest annual decline since the epidemic's peak in 2004 and 2005, and marked a 35-percent drop from the 2.4 million deaths seen in both those years.
New infections also fell to 2.1 million last year, down 38 percent 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.
UNAIDS said the battle needed to focus squarely on 15 countries which accounted for three quarters of new infections.
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.
The Geneva-based World Health Organization has called for greater efforts to treat gay men, transgender people, prison inmates, people who inject drugs and sex workers, who together account for about half of new HIV infections.