The 19-times grand slam champion opened up a 4-1 lead in the tiebreaker of an evenly-matched first set but Sock levelled at 4-4 with a flurry of powerful drives. Federer then took control, producing a neat backhand volley to close out the first set.
The second set went with serve up to 4-4 before Sock missed an opportunity to break. The American world number eight then double-faulted at 5-5 as Federer pounced to snatch a decisive break and went on to seal the win.
"I've maintained a high level in all three matches, which is a great thing," Federer said after the match.
"This was another step up in terms of ranking and I thought it was a very entertaining match for both of us... I thought it was a good step forward."
Bencic secured the victory for Switzerland with a 7-6(6) 6-4 win over Vandeweghe. Federer and Bencic then won the dead mixed doubles rubber 4-3(3) 4-2.
Group B winners Switzerland will face the winner of Group A in Saturday's final, with Germany, Belgium and Australia all capable of sealing top spot.
Earlier, Naomi Osaka ground out a 6-4 3-6 7-6(5) win over Anastasia Pavlyuchenkova but Japan failed to capitalise on the early advantage as they lost 2-1 to Russia.
Karen Khachanov thumped Yuichi Sugita 6-4 6-2 before teaming up with Pavlyuchenkova to beat the pair of Sugita and Osaka 4-1 4-0 in the mixed doubles rubber.
(Reporting by Shrivathsa Sridhar in Bengaluru Editing by Jeremy Gaunt.)
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