The all-star American quartet -- including 100m world champion Christian Coleman and 200m gold medallist Noah Lyles -- never looked in trouble in winning the title for the eighth time.
"We are a brotherhood," said 2017 100m world champion Justin Gatlin.
"We had a talk this morning and we said we are going to go out there and do this.
"I wanted it especially hard as I have never won a relay title."
Veteran Michael Rodgers said they had been motivated by one thing.
"We wanted to do this for Justin."
Defending champions Britain took silver as Nethaneel Mitchell-Blake ran a superb anchor leg to overhaul Japan's Abdul Hakim Sani Brown.
Both the British and the Japanese set new European and Asian records with times of 37.36sec and 37.43sec respectively.