Lyles added the relay gold to his sprint double while Richardson had already claimed 100m gold and bronze in the 200m.
It was a glorious end to the night for the sport's superpower after the earlier disappointment of seeing their highly-favoured 4x400m women's team disqualified following a baton failure in the semi-finals.
But they were almost faultless on Saturday as Christian Coleman, Fred Kerley, Brandon Carnes and Lyles won in 37.38.
Olympic champions Italy, with Tokyo individual gold medallist Lamont Marcell Jacobs on the second leg, took silver with 37.62.
Richardson and Gabby Thomas were added to the women's team alongside Tamari Davis and Twanisha Terry and the foursome were superb in running a championship record time of 41.03 seconds.
Persons:
Richardson, Noah Lyles, Sha'Carrie Richardson, Lyles, Christian Coleman, Fred Kerley, Brandon Carnes, It's, Lamont Marcell Jacobs, Gabby Thomas, Tamari Davis, Twanisha Terry, I'm, Shericka Jackson, Alexis Holmes, Quanera Hayes, Holmes, Hayes, Mitch Phillips, Ken Ferris, Pritha
Organizations:
Jamaica, BUDAPEST, United States, Italy, Britain, U.S, Thomson
Locations:
Tokyo, Britain, Jamaica, U.S, Canada, India