Campbell held on in a dramatic race to the line with Jamaica's Asafa Powell.
Both men stopped the clock at 38.62 seconds, but Campbell's chest was shown to cross the line first.
Campbell was convinced he had won, but he and team-mates Jason Gardener, Marlon Devonish and Allyn Condon were made to wait for the verdict.
Michael Frater, Dwight Thomas, Chris Williams and Powell were forced to settle for silver, with Tim Williams, Paul Di Bella, David Baxter and Patrick Johnson taking third for Australia.
Canada came in fourth ahead of Trinidad and Tobago, Nigeria, Cameroon and Wales.