Eubanks, ranked No. 32 in the world, had seven aces while producing a 6-3, 6-2 victory over Ukraine's Viacheslav Bielinskyi to help the U.S. take a 2-0 lead in the best-of-five competition. It was the Davis Cup debut for the 6-foot-7 Eubanks.
Fritz, the top-ranked American men's player at No. 9, is dealing with a right hip injury.
Eubanks admitted to be antsy prior to the match.
"All day since I found out I was playing I was really nervous," Eubanks said. "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."
No. 33 Sebastian Korda also prevailed for the U.S. He had 16 aces while outlasting Oleksii Krutykh 6-3, 6-7 (3), 6-4 in the first match between the countries.
The Americans will seek to clinch a spot in the next round on Friday when the doubles duo of Austin Krajicek and Rajeev Ram faces Ukraine's Illya Beloborodko and Vitaliy Sachko.
This week's 12 winners advance to the 2024 Davis Cup Finals, along with reigning champion Italy, runner-up Australia and wild-card entrants Great Britain and Spain.
This should have been a road competition in Ukraine for the Americans, but matches are being played in Vilnius due to the ongoing war in Ukraine.
