Coleman, world 100m champion, put the Americans ahead with a stunning start and 200m gold medallist Noah Lyles completed the job, crossing the line with his arms raised triumphantly in the air as his team mates celebrated wrapped in American flags.
"We were all motivated to do something special and it just happened, everybody wanted it," said Lyles, who will leave his first world championships with double gold.
"We all wanted to break the curse, a generational curse and bring on a new era," he added.
That is the part that feels the most exciting to think the time we break the curse is the time something great happens.
"Every time you come across in the relay with the USA it is magical, all of a sudden you get this energy to run around the track again."
Defending champions Britain took the silver in 37.36 seconds, a European record, as Nethaneel Mitchell-Blake failed to catch Lyles on the final straight.
Japan won bronze with a time of 37.43 seconds, an Asian record.
Joining Coleman and Lyles, the two rising stars on the global sprint scene, were veterans in Justin Gatlin, twice world champion, and 34-year-old Mike Rodgers, who had never before stood atop a world championship or Olympic podium.
After a wobbly performance in the heats in which Canada filed a protest against the U.S. for failing to make a proper exchange, the American quartet had a meeting to ensure there were no hiccups in the final.
Victims of sloppy exchanges and dropped batons over the years, the message came through loud and clear as the United States made four clean exchanges in a polished effort to come home just outside Jamaica's world record 36.84. "We had a meeting in the morning," said Coleman, who also heads home with two golds.
"We just got to come together, everybody just got to execute, focus on what they need to do, have an open dialogue about what went wrong in the prelims and what we are going to do better in the final.
"If you never have that conversation then you are just going to go there and you kind of can't expect different results," Coleman added.
"So we just got to talk about what we needed to do and everybody locked in and we got it done." (Reporting by Steve Keating and Gabrielle Tétrault-Farber, editing by Ed Osmond)