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The athletes were forced to restart after Hudson-Smith squirmed in the blocks, which resulted in a yellow card for the Brit.
Despite the disruption, Rooney, who failed to win at the Commonwealth Games in Glasgow, led the way to cross the finish line first in 44.71s.
Hudson-Smith took silver and set a new personal best time of 44.75s, while Donald Sanford of Israel nabbed the final spot on the podium by finishing third.
Britain's Conrad Williams crossed the line in fifth place.