On the first leg, American Noah Lyles separated from Bahamas' Blake Bartlett to his inside and gained on China's Tang Xingqiang, while Canadian Gavin Smellie gained against Jamaican relay gold medalist Nickel Ashmeade to his outside.
On the second leg, American Jarrion Lawson passed China's Mo Youxue, making USA look like the clear leader as the international broadcasters called the race.
On the inside, Canadian Brendon Rodney had also passed Jamaica's Rasheed Dwyer.
Canada put their star, triple Olympic medalist, Andre De Grasse on third leg.
Brown held that advantage to the finish line, with the Jamaican team, anchored by Yohan Blake, the second fastest man in history, trailing the Americans by 15 meters.