After Vanderweghe beat Lucie Hradecka 6-4, 6-2 to open the tie, Sock then edged past Adam Pavlasek in three sets.
The dead mixed doubles rubber was a relaxed affair played under the novel Fast Four format and the US came from a set down to win 2-4, 4-2, 4-1.
Sock, who is just one place in the rankings below last year's career-high of world number 22, traded winners with the inexperienced Pavlasek in the first set.
A break in the 11th game of gave Sock the advantage and the 24-year-old served out to clinch the set.
However, the 75th-ranked Pavlasek broke in the second game of the second set and fought back to level the tie.
Copyright Agence France-Presse, 2017