Nakashima beat Alejandro Tabilo 7-6 (7-5) 2-6 7-6 (7-3) after Reilly Opelka defeated Cristian Garin 6-3 4-6 7-6 (7-3) to give the Americans an early lead following the two hour, 26-minute opener.
The two singles matches lasted in excess of five hours, and there was a doubles match still to be played.
Four groups are playing in four cities this week to qualify for the Final 8 knockout stage to be held in Malaga, Spain, in November. The top two countries in each four-team group will advance.
The US, who have a leading 32 Davis Cup titles - the most recent in 2007 over Russia - are bidding to reach the quarter-finals for the second time since the Davis Cup Finals were introduced in 2019.
In the qualifiers this year, the Americans defeated Ukraine 4-0 on neutral ground in Vilnius, Lithuania.
Later Wednesday at Bologna, hosts Italy are scheduled to play Brazil in Group A.
At Valencia, Spain are set to play Czech Republic in Group B while Britain meet Finland in Group D in Manchester.
In opening play on Tuesday, Belgium beat the Netherlands 2-1, Australia defeated France 2-1, Germany, playing without No.2-ranked Alexander Zverev, beat Slovakia 3-0 and Canada defeated Argentina 2-1.
Italy won the 2023 title, beating Australia in the final.
