American Felix, 26, was second in the 200m in Beijing and has won three World Championship titles at this distance.
But she was brilliant in London, overhauling 100m champion Shelly-Ann Fraser-Pryce to win the Olympics at the third time of asking in a time of 21.88 seconds.
Another American, Carmelita Jeter, claimed bronze to add to her silver from the 100m.
Defending Beijing champion Veronica Campbell-Brown was run into fourth, with Sanya Richards-Ross of the USA fifth.
"It's been a long time coming. I am so overjoyed," said Felix, who lost her world titles to Campbell-Brown last year in Daegu. "I thought back to the disappointment in Beijing, it's been a long road, I never wanted to give up.
"I've wanted it for so long. This moment is really priceless."
Antyukh of Russia held off a late challenge from the USA's Lashinda Demus in a similarly thrilling women's 400 metres hurdles final.
Antyukh - a 400 flat runner who took up hurdles in 2009 and only became a contender this year - powered into the final hurdles with a good lead over Demus but had to resist a spirited late charge from the American to dip home in 52.70 seconds, smashing her personal best by almost a quarter of a second.
Zuzana Hejnova of Czech Republic was third in 53.38s.
It was easily the 31-year-old Antyukh's biggest career win, her previous triumphs including a 2010 European title in this event and several medals as part of the Russian 4x400m relay team.
"I was going to finish my career here but now I will think about it - maybe not," Antyukh said afterwards. "I have done a lot of work, to get a personal best is amazing - a world record soon would be great. It's not very far away."
She added that she would unlikely be at Rio de Janeiro in four years, saying she would like to have a family.
Demus, meanwhile, had failed to even qualify for the last Olympics in Beijing so will see silver as a triumph. The defending champion from 2008, Melanie Walker of Jamaica, was unable to get past the semi-finals this time out.
America's world indoor and outdoor champion Brittney Reese added an Olympic long jump gold medal to her growing list of titles with the second biggest jump in the world this year.
The 25-year-old only managed to register two of six attempts all night inside London's Olympic stadium but her second jump of 7.12 metres was good enough to take gold.
Russia's Elena Sokolova produced a personal best of 7.07 - the seventh best jump in the world this year - to claim silver with Reese's American compatriot Janay DeLoach taking bronze on 6.89.
Reese, who has this year's biggest leap of 7.15 metres, has back-to-back indoor and outdoor world championships in what has been a rich vein of form since finishing fifth in the 2008 Olympic final in Beijing.
She became the first American Olympic women's long jump champion since Jackie Joyner-Kersee in 1988 in Seoul.
Britain's Shara Proctor finished ninth after disappointing following an impressive qualification.
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