The 28-year-old hurdler produced a fine third leg in the final yesterday (Sunday) in Beijing to help the GB quartet - which also included Christine Ohuruogu, Anyika Onuora and Seren Bundy-Davies - to a season's best time of 3:23.62.
That was enough to hold off the challenge of Russia, who finished 1.22 seconds behind in fourth, as Child and her team-mates joined race winners Jamaica and silver medalists the United States on the podium.
The result was a repeat of Child's success in the 2013 World Championship in Moscow and came after the current European 400m hurdles champion finished sixth in the final of her individual event on Wednesday.
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