The Swedish team was made up of Anna Haag, Ida Ingemarsdotter, Charlotte Kalla and Emma Wiken.
That quartet won by a half second over Finland. Germany took the bronze, finishing nine-tenths of a second behind Sweden.
Norway was the defending champion in this race and had failed to medal in it just once in the last nine Olympics. The Norwegians finished fifth, almost a minute out of the lead.
Kalla became the first athlete at the Sochi Olympics with three medals. She won a silver in both the skiathlon and the 10-kilometer classic race.