The former heptathlete, who claimed silver in the 100 behind Shelly-Ann Fraser-Pryce on Monday, surged through the line in 21.63 seconds, the quickest time for 17 years in the half-lap sprint.
Only Americans Florence Griffith-Joyner, the world record holder, and Marion Jones, who was later banned for doping, have run faster.
"I can't believe it," Schippers told reporters. "What a race! What a tournament for me! I think they'll be going crazy in the Netherlands at the moment."
Thompson, 23, was second in a personal best 21.66 while bronze went to her compatriot, twice Olympic champion Veronica Campbell-Brown, in 21.97.
Schippers, taking part in her first major global championships as a sprinter, made a good start but had plenty to do to catch Thompson when they came off the bend.
The tall 23-year-old got into her powerful stride, however, and ate up the ground to overhaul her rival as she dipped for the line.
"Wow! Wow! Wow!" said Thompson, a student. "It has been a good feeling to compete with these ladies. Schippers is a great competitor. I am very, very pleased.
"After 100 metres I fought to keep Schippers away but I could not run faster than I did."
Schipper is the first European to win the title since Russia's Anastasiya Kapachinskaya in Paris in 2003, breaking 12 years of American and Jamaican dominance in the event.
"I stayed relaxed in the last 30, 40 metres and that's why I won," she added. "Tomorrow I'm joining up with the relay team and hopefully we can go for a medal."
American Candyce McGrone was fourth in 22.01, her career best, with teenager Dina Asher-Smith fifth in a British record 22.07, having improved her personal best for the third time in three days.
Fraser-Pryce, the 2013 champion, decided against doubling up in Beijing while the schedule prevented Olympic champion Allyson Felix running the 200 and 400 and she chose the longer race, winning gold on Thursday.
What was considered a weakened field produced one of the most thrilling and fastest races of recent world championships.
It featured two of the five fastest 200 metres of all time and six of the seven fastest of 2015 including the top four.
(Editing by Ed Osmond)
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