Thompson won the gold medal in a time of 10.71 seconds, with American Tori Bowie finishing second in 10.83.
Fraser-Pryce was attempting to become the first athlete to win the 100m at three successive Games, but she was forced to settle for bronze.
Compatriot Usain Bolt will be looking to achieve the same feat when the men's event concludes Sunday.
After joining Bolt as an Olympic champion, Thompson's thoughts immediately turned to the celebrations in her homeland.
"When I crossed the line and glanced across to see I was clear I didn't quite know how to celebrate," said the 24-year-old.
"There is a big screen back home in my community in Jamaica. I can't imagine what is happening there right now."
Despite failing to add to her wins in 2008 and 2012, Fraser-Pryce described the bronze as her "greatest medal ever" after an injury-interrupted 12 months.
"By far, I would definitely say that this is my best championship ever, because I knew how hard I worked, I knew the pain and and the sacrifices and the tears," said the 29-year-old.
"I knew everything and despite everything I stuck to it. I kept my head in the game. I am really happy that I persevered."
On a night of high drama, Britain's Mo Farah recovered from a trip midway through the 10,000m final to successfully defend one of the two titles he won at London 2012.
A coming together with former training partner Galen Rupp set Farah tumbling to the ground but he was able to get back on his feet and eventually overhaul Kenya's Paul Kipngetich Tanui.
Farah insisted he didn't blame Rupp for the incident, instead suggesting it was the result of his own long stride, while also revealing his daughter was the motivation behind his comeback.
"At one moment I was thinking my race is over, my dream is over," said the Somalian-born 33-year-old. "I managed to dig deep. I promised my little daughter Rhianna a medal, my mind was on that. 'You can't let her down, you can't let her down'.
"The twins from 2012, have got one (medal) each so I was like 'Rihanna is missing one', so I was like I can't, I can't let her down'. That is why I was quite emotional at the end."
Farah's compatriot Jessica Ennis-Hill failed to defend her Olympic title as Belgium's Nafissatou Thiam set five personal bests across the seven heptathlon disciplines on her way to gold.
Ennis-Hill needed to beat Thiem by 9.47 secs in the final event, the 800m, to finish top of the podium. But Thiem was able to dig deep and secure a breakthrough triumph.
"At first I did not want to think about a medal," said the 21-year-old
"After the long jump I thought a podium finish is possible, but not the gold medal. After the javelin I thought, gold is possible. In the 1500m I gave everything I had and now it is gold."
There was also a tense finish in the men's long jump as American Jeff Thompson leaped to glory with a jump of 8.38 meters.
His teammate Jarrion Lawson thought he had done enough to snatch the gold with what looked like a big final-round jump.
But his celebrations were cut short after his hand brushed the sand as he landed in the pit, significantly shortening the distance recorded and meaning he finished outside of the medals.
"It was very close," Henderson said of Lawson's jump. "That was a long jump. Heard it was his hand or something -- this happens in long jump, I'm sad it happened to him."
Britain's Greg Rutherford was distraught after losing his Olympic title, despite winning his country's third track and field medal of the day with a bronze while South Africa's Luvo Manyonga finished second.