The 24-year-old clocked 10.71 seconds to hold off the US' Tori Bowie, who took silver in 10.83 on Saturday, reports Xinhua.
"When I crossed the line and glanced across to see I was clear, I didn't know how to celebrate," Thompson said.
Thompson's fellow Jamaican Shelly-Ann Fraser-Pryce, winner of the previous two Olympic gold medals in the event, had to settle for bronze in 10.86.
Marie-Josee Ta Lou of Cote d' Ivoire was fourth and Dafne Schippers of the Netherlands fifth.
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