After Jamaica’s world champion Shericka Jackson withdrew before the race, American Thomas was regarded as the favourite. She dominated the final, winning in 21.83 seconds.
Neita, who missed out on a 100m bronze medal by four hundredths of a second on Saturday, and Asher-Smith were both aiming to become the first British woman to reach the Olympic sprint podium in 64 years.
However, Asher-Smith placed fourth in 22.22 and Neita finished fifth in 22.23, trailing runner-up Julien Alfred (22.08) and American bronze medalist Brittany Brown (22.20).
Thomas had to settle for world silver behind Jackson last year, after taking Olympic bronze.
But, as the fastest woman this year and in the absence of her primary challenger, the 27-year-old screamed a victorious roar crossing the finish line and held her hands on her head in surprise after grabbing her opportunity.
I’ve replayed this race in my head numerous times, like I do with every race, and that’s how I win races, said Thomas. “But I didn’t expect to feel like I did when I passed that line.
I could not believe it. I never believed in my wildest dreams that I would win an Olympic gold medal. It was the happiest time in my life.