The US men have not won the event they formerly dominated since 2000 but Christian Coleman, making his first appearance of the Games, set them on their way well.
Fred Kerley, who was involved in the botched changeover that ended their Tokyo hopes, ran a strong second leg, handing to green-haired Kyree King, and Courtney Lindsey brought them home well clear in 37.47 seconds.
Akani Simbini ran a storming last leg to take South Africa to second in 37.94, just ahead of Britain (38.04).
A slick China won the second heat in 38.24 and France were roared to second in 38.34 but Jamaica, champions in 2012 and 2016, messed up two changeovers to finish fourth and miss out on Friday’s final.
The US women took gold ahead of their big rivals in 2012 and 2016 but were knocked back into second in Tokyo.
Jamaica, however, are shorn of the superstars who brought them home three years ago, while the US were able to field an immensely powerful and in-form quartet.
Melissa Jefferson (third in the 100), Twanisha Terry (fifth in the 100), Gabby Thomas (200 gold medallist) and Sha’carri Richardson (silver in the 100) make up the team, the last three having won world gold in the relay event last year.
They sailed close to the wind with the second changeover as Terry struggled to catch Thomas, losing considerable ground to Germany, which Richardson duly made up with a terrific last leg as they qualified fastest in 41.94 seconds.
Britain, bronze medallists in the last two Games, made it through as winners of the second heat in 42.03 and will be considerably strengthened by the return of Dina Asher-Smith and Daryll Neita for the final.
There was plenty of noise too for second-placed France (42.13), with Jamaica struggling home a distant third in 42.35.
Canada finished fourth in a national record of 42.50 to go through to Friday’s final as a fast loser.
