Richardson, Thomas guide US women into 4x100m relay final
Melissa Jefferson, who won bronze in the 100m in Paris, ran the opening leg, with Twanisha Terry taking the baton down the far straight.
Terry's handover to Thomas wasn't as smooth as it could have been, however, handing the advantage to Germany.
Thomas' pass to anchor-leg Richardson was clean.
The 100m silver medallist then powered past Rebekka Haase to push the German quartet into second in 42.15.
Switzerland took the third automatic qualifying spot.
Britain won the second semi-final in 42.03sec ahead of France and Jamaica, the reigning Olympic champions but missing big guns such as Shelly-Ann Fraser-Pryce, Shericka Jackson and Elaine Thompson-Herah.
Canada and the Netherlands sealed the two fastest non-automatic qualifying places for the final scheduled for 1730 GMT on Friday.
Noah Lyles' bid for a first triple sprint gold since Usain Bolt at the 2016 Rio Games remains on track thanks to his US teammates Christian Coleman, Fred Kerley, Kyree King and Courtney Lindsay.
That American quartet clocked 37.47sec to win their semi-final and book a place in the final to be held 15 minutes after that of the women.
Lyles won the 100m in a dramatic photo-finish on the weekend and goes into the final of the 200m later Thursday as hot favourite. Come the relay final, he will undoubtedly run the anchor leg.
China won the second semi in 38.24sec ahead of France and Canada. Jamaica, with 100m silver medallist Kishane Thompson on anchor, finished fourth and failed to advance.
Also qualifying as the two next fastest were Japan and Italy, for whom Tokyo Games 100m gold medallist Marcell Jacobs ran the opening leg.