Richardson wins second gold as she anchors USA to women's world relay title
Richardson was pressured by Jamaica's 200m champion Shericka Jackson down the straight but she held her off with the USA's arch-rivals taking silver in 41.21sec.
Britain won the bronze in a time of 41.97sec.
The USA quartet broke the Jamaican's championship record that had stood since 2015 in Beijing.
"We're not disappointed," said Jamaica's Shashalee Forbes, who ran the third leg.
"It was a great race. They were very tough. We went out to deliver and we are happy and pleased with what we got."
The Jamaicans may come to regret omitting two-time Olympic 100m champion Elaine Thompson-Herah, who ran a cracking second leg in the heats on Friday.
The Americans, though, were in command from the off and had a sizeable lead when Richardson took the baton from 200m silver medallist Gabby Thomas.
Once again Jackson, who had run the second fastest time ever in the 200m final on Friday, could not match Richardson and made little impact.
Richardson's momentum over the line carried her right into the USA men's quartet who were celebrating their own relay victory.
She hit Christian Coleman full on, both crashing to the track, but was quickly lifted back up and embraced by the men's team and her own female teammates.
There was some consolation for Jamaican sprint legend Shelly-Ann Fraser-Pryce as she claimed her 16th world medal, to move one ahead of her retired fellow legend Usain Bolt.
American icon Allyson Felix holds the record, with 20 medals.