Sam Querrey leveled for the Americans by beating Daniel Gimeno-Traver 6-3, 6-4, after Spain's Nicolas Almagro saved a match point before overcoming Robby Ginepri 6-3, 5-7, 7-6 (4).
The best-of-three series will be decided by a doubles match Wednesday.
Also in the Red Group, the Czech Republic leads Australia 1-0 after Jan Hajek overwhelmed Peter Luczak 6-1, 6-2.
In the Blue Group, Germany leads Argentina 1-0 after Philipp Kohlschreiber defeated Horacio Zeballos 6-3, 6-4, and France and Serbia are level at 1-1.
Paul-Henri Mathieu beat Dusan Lajovic 6-2, 6-3 before Viktor Troicki leveled for Serbia by beating Jeremy Chardy 6-4, 6-2.
Querrey was always on top against Gimeno-Traver, breaking for 4-2 in the opening set and staying ahead in the second after the first three games went against serve.
Ginepri had little to show for his efforts against Almagro. The American held five break points in the first set before Almagro broke to lead 4-2. Ginepri held the only break points of the second set at 6-5, converting when Almagro made a forehand error.
After an early exchange of breaks in the final set Ginepri held a match point at 6-5, which Almagro fought off with a backhand winner, and the Spaniard went on to take the tiebreaker.
Ginepri had not expected to be playing in the competition, only arriving in the city the previous evening from Paris. He only discovered on Monday that he had a place in the main draw for the French Open and would not need to go through qualifiying. He quickly accepted an invitation from Querrey to head for Duesseldorf.
"I'm pretty happy with the way it went today," Ginepri said. "A little unfortunate I didn't come out with a victory, but he's one of the better clay courters out there. So, I'll take a lot of positives from this match."
Each match in the round-robin format consists of two singles and a doubles, played over two days. The winner of each group will meet in Saturday's final.
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