Keys' victory handed the defending champions an unassailable 3-1 lead over France in the semi-final tie before the hosts won the dead doubles rubber.
The French pair of Amandine Hesse and Kristina Mladenovic edged Vandeweghe and Bethanie Mattek-Sands 6-4 3-6 10-6.
Earlier in the day, U.S. Open champion Sloane Stephens thrashed Mladenovic 6-2 6-0 to collect her second singles victory this weekend.
Stephens was aided by 25 unforced errors from world number 20 Mladenovic, whose touch eluded her far too often in the match.
"That was a really good one. You never anticipate a scoreline like the way it turned out but it was really solid," Stephens said.
The Americans extended their winning record to 12-2 against the French.
They will defend their title on Nov. 10-11 against the Czech Republic, who reached the final by defeating Germany 4-1 in Stuttgart.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
