The three fastest in the world this year lined up side by side in the second heat but American Richardson was left for dead at the start as Jamaican Jackson, the world leader, and Ivorian Ta Lou were a metre up before she was upright.
Jackson was clear and eased at the end, allowing Ta Lou to exactly match her 10.79 finishing time, even to the thousandth of a second.
A desperate Richardson had to strain every sinew to claim third in 10.84 – which proved good enough to send her through as one of the two fastest losers.
Jamaica's Shelly-Ann Fraser-Pryce, seeking a remarkable sixth title at 36, looked totally relaxed as she got things moving with a comfortable-looking 10.89 in the first heat.
She recovered from a sluggish start to drive home, with American Tamari Davis (20) going through alongside with 10.98.
Julien Alfred (22) of St Lucia had a scare, being given a warning card after moving in the blocks in the third heat. She then had a terrible start in the restarted race but finished well to win in 10.92.
Dina Asher-Smith (27) and Poland's Ewa Swodoba (26) clocked 11.01 and, though the Briton's time was a thousandth quicker, both were advanced to the final on the nine-lane track, which takes place later on Monday at 20:50 CET.
