Hamilton, whose paternal grandparents are Grenadian, clocked one hour, 36:52.941 seconds for his third successive third placed finish, to move to the top of the drivers standings.
Rosberg, meanwhile, clocked 1:36:26.929 while Hamilton’s McLaren teammate and fellow Brit Jenson Button was second in 1:36:47.555.
“I had a great race and although neither Jenson nor I was sadly able to win, I’m really happy that Nico took his first win today,” Hamilton said afterward.