Fognini broke a two-match losing streak at the inaugural tournament for the tie-clinching win by defeating America’s John Isner for the first time, 6-4, 7-6(5).
Travaglia had started Italy’s winning streak by beating America’s Taylor Fritz in the first singles match.
“I was feeling good from the beginning,” Travaglia said after his victory.
“I was feeling good with the return first and with my serve too – better than in the past two matches.
“I think I adapted very well in these conditions in the evening, no wind, no heat and it was slower.
“The courts were slower than the practice court... I think it is my best result of maybe the past two years.
“I’m very happy of this result.”
Simone Bolelli and World No. 12 Fognini then won the doubles 6-4, 6-7(5), 10-3 over Austin Krajicek and Rajeev Ram for Team USA.
Despite these performances, Italy cannot qualify for the Final Eight as fellow second-placed countries Belgium and Canada own better records heading into Day 6 on Wednesday.
