Heading into the competition at Val di Fiemme America had yet seen one of their athletes climb the top step of the podium at a World Championships or Olympic Games.
Randall had won a sprint silver in the 2009 World Championships - but went one better alongside Diggins in Italy.
The duo crossed the finish line in 20:24.44 for the win, Sweden's Charlotte Kalla and Ida Ingemarsdotter 7.80 seconds further back in second with Finland's Riikka Sarasoja-Lilja and Krista Lahteenmaki taking bronze.
In the men's event it was Russian duo Alexey Petukhov and Nikita Kriukov who claimed the gold.
The pair crossed in 21:30.98 for Russia's first team relay gold medal in a major championship since 1982.
Sweden once again had to settle for silver as Marcus Hellner and Emil Joensson crossed in second, with Kazakhstan's Nikolay Chebotko and Alexey Poltoranin picking up bronze.
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