The 25-year-old American rose from one of the two trackside seats reserved for the fastest losers, having sat through the other two semi-finals, and did an impression of aiming a fist at a punching bag.
Richardson, last year's Olympic silver medallist, had a dreadful start after receiving a warning for falling over the start line, but she fought her way into third spot to a time of 11.00 seconds.
Veteran Marie-Josee Ta Lou-Smith, a 100m world silver medallist in 2017, and Jamaica's Shericka Jackson, herself a two-time runner-up in the 100m final, took the automatic spots.
Neither of them looked as sublime as Olympic champion Julien Alfred, who eased to victory in her semi-final.
For five-time 100m world champion Shelly-Ann Fraser-Pryce, there will be a last major individual championship final, as the 38-year-old Jamaican legend took second behind Alfred.
As Richardson gritted her teeth in the seat, the eight runners in the third semi - including teammate and the form sprinter of the season, American Melissa Jefferson-Wooden - took to the blocks.
Jefferson-Wooden, unlike Richardson, made a dream start and the 24-year-old was easing down as she took the tape in 10.74 seconds with Jamaica's Tina Clayton finishing second.
Third-placed Dina Asher-Smith and Richardson, still seated, looked anxiously at the board until the latter rose to her feet when she saw 11.02 seconds come up.
Asher-Smith, the silver medallist in the 2019 world 100m final before winning the 200m gold, gave a shake of her head as she realised her going through was at the cost of British teammate Amy Hunt.