Bolt's task was made easier when American fourth-leg runner Justin Gatlin fluffed his start, stumbling and veering into the Jamaican's lane.
"We could have gotten the Jamaicans," said a rueful Gatlin, runner-up to Bolt in the 100 final.
"I'm disappointed (for my team mates). They deserved more. I think my stumble cost us victory."
The Jamaican quartet of Nesta Carter, Kemar Bailey-Cole, Nickel Ashmeade and Bolt secured the Caribbean nation a hat-trick of world titles in a time of 37.36.
Gatlin brought home the U.S. in 37.66 with Canada upgraded to bronze after Britain were disqualified, continuing their relay woes of past championships in which they have often failed to get the baton around a full lap.
The Britons were penalised after a changeover mistake between Harry Aikines-Aryeetey and James Ellington who minutes earlier had told the BBC that the team had "got the changeovers down to a tee now".
It was a measure of consolation for the Canadian men who were disqualified for a lane violation after finishing third in last year's Olympic final.
The Jamaican women regained the world title from the U.S., again helped by a costly error.
The quartet of Carrie Russell, Kerron Stewart, Schillonie Calvert and Fraser-Pryce streaked to gold in 41.29, the second fastest time ever run.
A mishap on the second and third interchange between Alexandria Anderson and English Gardner who started her run too soon and had to halt to grasp the baton, effectively ended U.S. victory hopes.
A storming final leg from Octavious Freeman secured third at the line, Freeman eating up ground down the home straight with a sizzling run.
France crossed in second place but were disqualified after the medal ceremony, the U.S. upgraded to silver and Britain bronze.
The British team filed a protest against the French team, saying they had changed outside the sector in the second baton exchange.
France were then disqualified and launched an appeal which was rejected.
The U.S. set a stunning world record of 40.82 at the London 2012 Olympic Games but none of that victorious quartet featured in the Moscow final, notably Allyson Felix who tore a hamstring in the 200m final and 100m bronze medal winner Carmelita Jeter who was left out.
(Editing by Alison Wildey and Ed Osmond)
