Sebastian Korda and Davis Cup debutant Chris Eubanks won Thursday's singles matches as the United States moved 2-0 up against Ukraine in their qualifier in Lithuania.
World number 33 Korda overcame the challenge of Oleksii Krutykh, a player ranked 309 places beneath the American, to earn a battling 6-3, 6-7 (3/7), 6-4 victory in the opening rubber.
Eubanks stepped in for the injured Taylor Fritz and beat 498th-ranked Viacheslav Bielinskyi 6-3, 6-2 to leave the record 32-time winners in sight of the September finals featuring 16 teams.
"All day since I found out I was playing I was really nervous," said Eubanks.
"Representing your country means a lot more than just playing for yourself. I had a lot of guys I didn't want to let down. Nerves were pretty strong at the beginning but once I got on court I settled down nicely and played pretty well."
Austin Krajicek and Rajeev Ram can seal the tie in Saturday's doubles, which takes place before the reverse singles.
The US have not won the title since 2007.
Defending champions Italy and last year's runners-up Australia, as well as Britain and Spain have advanced automatically to the finals.
Serbia will be without Novak Djokovic as they attempt to clinch one of the remaining 12 qualifying spots against Slovakia.
Alexander Zverev is missing from the Germany team for their tie against Hungary due to illness.
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