Fox, from Hendersonville, Tenn.; Williams, from Moscow, Idaho; and Justin Thomas of Goshen, Ky., combined for a 54-hole total of 24-under 404. Thomas shot a non-counting 70 on Sunday.
They teamed to beat Mexico by five strokes at Antalya Golf Club to give the United States it 14th Eisenhower Trophy title.
"It's fun to win as an individual," said Williams, a senior at the University of Washington. "But to win as a team is awesome and it doesn't get any better than doing it as representative of the USA."
The Americans also broke the records for 18 and 36 holes.
"I would go back to the first round where Chris shot 64 and Justin shot 67 and we were 13 under," Fox said. "We just built from there."
Mexico's Sebastian Vazquez was the low individual at 15-under 199.