The battle between Gatlin, the 35-year-old 2004 Olympic 100m champion who has served two doping bans, and Usain Bolt's self-professed successor Andre de Grasse did not play out, the Canadian deprived of the chance to run his leg after a botched handover by his teammates.
De Grasse, a three-time medallist at the Rio Olympics, had cocked his head over towards Gatlin three times before turning on the afterburners to edge the American in the heats.
The US were not out of danger, however, with Britain looking to be ahead as Gatlin took the baton from Ronnie Baker after slick passovers between Leshon Collins and Mike Rodgers.
But Englishman Danny Talbot failed to hit his mark and Gatlin had a free run in for 38.43sec, eyes glued on the big screen in near bewilderment as Barbados took silver at a distant 39.12 and China bronze (39.22).
Thompson, who won double gold in Rio last year, was afforded a rousing welcome as she safely led her Jamaican teammates to victory in the women's 4x200m.
"There was no pressure," said Thompson. "We came on the track and do what we do."
The US defended their women's 4x800m relay title in first final of the night, Laura Roesler and Charlene Lipsey pulling away in the final two legs after teammates Chanelle Price and Chrishuna Williams were involved in an early nip-and-tuck battle with Australia.
"I've had the pleasure of making all three teams that have won here in the Bahamas," said Price, whose opening leg of 2:01.73 was the quickest run on the night.
Belarus eventually edged the Australian quartet into third thanks to a strong anchor leg by Maryna Arzamasova, the 2015 world champion in Beijing.
- Heartache for Shaunae -
=========================
Despite Olympic 400m champion Shaunae Miller-Uibo running a scorching first leg, the Bahamas failed to progress to the final of the women's 4x400m. France, with European indoor champion Floria Guei running anchor, also failed to qualify.
There was also no such luck for the Jamaican men's 4x100m quartet, missing Bolt and late withdrawal Asafa Powell, as the precision needed for baton passovers was highlighted in their first-round race.
"We didn't get here in time to practise," said Minzie, the team having had just one previous outing. "It was just a misunderstanding. It happens in relays," added the last member of the team, Everton Clarke.
That leaves the Jamaicans needing to post a top-16 qualifying time for the London worlds by July 23.
Sunday's action sees the men compete in the 4x200m, 4x400m and 4x800m and the women in the 4x100m and 4x400m, while there will also be a mixed-sex 4x400m relay, handing Miller-Uibo a second chance to shine in front of her raucous home support.
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