She became the first short track skater to win two individual gold medals at the same Olympics.
Ko Gi-Hyun of South Korea, the 1,500 metres gold medallist, grabbed the silver while China's Yang Yang (S) took the bronze, her second of the Games.
Yang Yang (A), a five-time world champion, led from start to finish.
"If I had gotten the gold medal four years ago, I might have retired by now," said Yang, who revealed that she had been depressed after her disqualification in the 1,000m in Nagano four years ago.
"The last four years, I have skated with my heart. I have more passion for skating now," the 25-year-old added.
With a lap remaining, Yang Yang (A) assumed control and battled 15-year-old Ko to the finish.
After 10 silver medals and four bronzes, Yang Yang (A) gave China its first-ever gold medal by winning the 500 metres a week ago.
Yang Yang (A) is no relation to Yang Yang (S) - they use the initials tagged at the end of their names to differentiate themselves.