Playing on an indoor hard court at Prague's O2 Arena, the 24th-ranked Czech broke Shelton's serve early in both sets and maintained enough control to prevent the American from mounting a comeback.
The victory brought the Czech Republic back to 1-1 in the best-of-five series and denied Shelton a winning return to competition following his run to his first Grand Slam final at the US Open.
Shelton, who has risen to a career-high No. 4 in the world rankings after his impressive campaign in New York, was unable to turn his powerful serve into the weapon it has often been during his rise up the rankings.
The defeat also extended a difficult Davis Cup record for the 23-year-old American, who is now 0-3 in the competition.
His previous Davis Cup appearance came in the 2024 quarterfinals, when he lost both his singles and doubles matches alongside Tommy Paul as the United States was eliminated by Australia.
Earlier on Friday, Learner Tien had given the United States an ideal start on his Davis Cup debut, defeating Jakub Mensik 6-2, 6-4.
Tien's consistency proved decisive as he committed only 15 unforced errors compared with 34 from Mensik, allowing the American to control long exchanges and secure the opening point for his country.
But Lehecka's victory over Shelton ensured the Czech Republic remained firmly in contention.
The decisive stages of the tie will take place on Saturday, when the teams are scheduled to contest the doubles before returning to the reverse singles.
The winner will secure a place in the Davis Cup Final 8, which will be held in Bologna, Italy, in November.
South Korea Moves Closer to Historic Qualification
South Korea moved to within one victory of becoming the first Asian nation to reach the Davis Cup Final 8 after taking a commanding 2-0 lead over India.
The South Koreans had to fight back from a set down in both singles matches in Seoul.
Kwon Soon-woo recovered from losing the opening set to defeat Dhakshineswar Suresh 3-6, 6-3, 6-4 at the Olympic Tennis Center.
Hyeon Chung then completed another comeback, overcoming Sumit Nagal 2-6, 6-4, 7-5 to put South Korea in a strong position heading into Saturday's doubles and reverse singles.
India now faces the difficult task of winning the remaining matches to overturn the deficit and keep its hopes of advancing alive.
Other Davis Cup Qualifying Ties
Austria and Belgium finished the opening day level at 1-1, leaving their qualification contest finely balanced ahead of the remaining matches.
The other teams competing for places in the Final 8 are contesting the following ties:
- Chile vs Spain
- Germany vs Croatia
- Britain vs Ecuador
- Canada vs France
Germany will host Croatia in Halle on Saturday and Sunday, with world No. 3 Alexander Zverev scheduled to lead the German challenge.
The successful teams from the qualifying round will join host nation Italy, the three-time defending champion, in Bologna for the Final 8 in November.