Lorenzo Sonego and Jannik Sinner secured wins in their singles matches to give Group E hosts Italy a 2-0 lead against the US in Turin before losing the doubles in straight sets.
Sonego, 26, got off to a great start with a 6-3, 7-6 (7-4) win over Reilly Opelka.
“It was not easy to play here, but this crowd … It’s the first time in Davis Cup and I was so looking forward to this match – thank you everyone,” Snog said.
World No.10 Sinner then sealed the match, hitting 17 winners in a 6-2, 6-0 thrashing of John Isner.
“Playing here was very special,” Sinner said.
“Today we have won already, which is great. We have a great team and everyone is a great guy as well, so we are just trying to stay together. I am very honoured to be a part of this.”
In Madrid, Feliciano Lopez and Pablo Carreno Busta helped holders Spain to an 2-0 lead over Ecuador.
Lopez eased past Roberto Quiroz 6-3, 6-3 before Carreno Busta fought back from a set down to beat Emilio Gomez 5-7, 6-3, 7-6 (7-5).
Carreno Busta then returned for doubles action with Marcel Granollers as the Spanish duo won 6-4, 6-7 (7-5), 7-6 (7-2) over Gonzalo Escobar and Diego Hidalgo.
Earlier, Novak Djokovic overpowered Dennis Novak and Dusan Lajovic battled past Gerald Melzer as Serbia went on to a 3-0 win over Austria in Innsbruck.
“I felt very good. I was locked in from the first point, determined to execute the game plan,” Djokovic said afterwards.
“The crucial game was the eighth game of the first set, 4-3, new balls. I managed to put in a couple of extra returns, make him play, mix up the pace. After that, there was really no looking back. I just served well, moved great.”