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.
Meanwhile, a debut win for Billy Harris sealed victory for Great Britain in their opener against Finland in Manchester.
Harris held his nerve in a tight second set against Otto Virtanen to secure a 6-4 7-6 (6-4) victory and give the hosts an unassailable 2-0 lead in the tie.
The win, coupled with Dan Evans' 7-6 (3) 6-2 success against lowly-ranked Eero Vasa earlier ensured Britain avoided any missteps as they try to book their spot at the last eight event in Malaga in November.
Carlos Alcaraz clinched victory for Spain against the Czech Republic in Group B when Tomas Machac retired injured with the score at 6-7 (7-3) 6-1 in Valencia. It gave Spain an unassailable 2-0 lead, with Roberto Bautista Agut having already defeated Jiri Lehecka 7-6 (7-1), 6-4.
It was world No.2 Alcaraz's first match since losing in straight sets to Botic van de Zandschulp, who was ranked 74th, at the US Open.
Italy didn't need top-ranked Jannik Sinner, the newly crowned US Open champion, to beat Brazil in Group A in Bologna.
Matteo Berrettini beat Joao Fonseca 6-1, 7-6 (7-5) before Matteo Arnaldi gave Italy an unassailable 2-0 lead by beating Thiago Monteiro 7-5, 6-7 (7-4), 7-6 (7-5).
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.
