The Jamaican could afford to ease up near the line as she finished in 11.05 seconds while her main rivals also comfortably survived the first stage in front of a crowd of over 50,000.
American Tori Bowie, silver medallist behind Thompson in Rio last year, won her heat in exactly the same time.
Dafne Schippers, who unlike Thompson will run in both the 100 and 200 meters, started her bid for a double by finishing second in her heat in 11.08 seconds behind Ivorian Marie-Josee Ta Lou, still good enough to qualify comfortably.
Gina Lueckenkemper produced the most impressive performance as she won the first heat in a personal of best of 10.95 seconds, becoming the first German to break 11 seconds since Katrin Krabbe at the 1991 World Championships.
"It was amazing and I am absolutely speechless after that race," said the 20-year-old. "It was a dream to run sub-11 inside this stadium at these championships. This just feels so, so good."
It was a mixed day for Germany, however, as her compatriot Tatjana Pinto false-started in her heat and become the only athlete to be disqualified.
Britain's Desiree Henry, who as a 16-year-old was one of the torchbearers at the London Olympics five years ago,
also qualified after finishing fourth in her heat.
(Writing by Brian Homewood, editing by Pritha Sarkar)
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