The Dominican Republic's Felix Sanchez was beaten in the 400m hurdles though, while Olympic 1500m champion Taoufik Makhloufi of Algeria, running in the 800, was upstaged by 18-year-old Ethiopian Mohammed Aman.
They were among 11 Olympic champions running at the Stockholm Olympic stadium which staged the Games in 1912 having been opened one month earlier.
American Richards-Ross was trailing off the final curve before powering down the final straight to take victory from Botswana's Amantle Montsho in 49.89 seconds while Britain's Olympic silver medallist Christine Ohuruogo was third.
Russia's Zaripova, who set the previous world leading time in winning Olympic gold, bettered that performance by running nine minutes 05.02, beating Tunisia's Habiba Ghribi into second place as she did in London.
Sanchez, whose tearful reaction to winning Olympic gold was one of the most emotional moments of the Games, lost to American Michael Tinsley, the man he beat into second place in London.
Olympic champion Christian Taylor of the United States won the men's triple jump while Olympic shot put champion Tomasz Majewski of Poland had to settle for second place behind American Reese Hoffa's first throw of 21.24 metres.
The women's discus and shot put produced a repeat of the one-two combinations in London.
Croatia's Sandra Perkovic won the discus with her final throw of 68.77m ahead of Russia's Darya Pishchalnikova who had to be content with second place.
New Zealand's Valerie Adams again emerged victorious in the shot with a throw of 20.26m ahead of Russia's Evgeniia Kolodko.
Russia's Anna Chicherova was another Olympic champion to win as she triumphed in the high jump with a 2.00m leap.
But Olympic champion Jennifer Suhr of the United States had an unhappy evening in the pole vault, entering the fray at 4.55m and failing to clear that height as London Games silver medallist Yarisley Silva of Cuba won with 4.70m.
Women's Olympic long jump champion Brittney Reese also fared poorly as she came ninth in an event won by Russian Yelenka Sokolova.
- Stockholm Olympic stadium