Taylor Fritz broke Jiri Leheka in the ninth game of the second set to beat the Czech 6-3, 6-4 to give the United States a 1-0 lead in their mixed team United Cup matchup on Thursday.
Madison Keys will take on Marie Bouzkova in the next Pool C match at the Roswell Arena with the United States leading 2-0 on the opening day.
Two singles matches – one for men and one for women – will be held over two days and the second day of mixed doubles will conclude the five-match series.
The United States is the third seed in the tournament, along with Jessica Pegula (3) and Frances Tiafoe (19). Czech Republic is seeded 14th.
In the first United Cup, teams from 18 countries will play in Brisbane, Perth and Sydney till January 4. The champions of the three cities and the next best country from the group stage will advance to meet at the Ken Rosewall Arena on January 6-8 to determine the champion.
Greece, the first seed, is led by Stefanos Tsitsipas (3) and Maria Sakkari (6). World number one Inga Swiatek and Hubert Hirkaj (11) are ahead of second seed Poland.
Rafael Nadal will pair up with Paula Badosa (13) for Spain, while Italy will be represented by Matteo Berrettini (16) and Martina Trevisan.
Each city will have two groups of three nations that will compete in a Roden-Robin format.
Other matches on Thursday saw Italy v. Brazil in Group E in Brisbane, Switzerland against Kazakhstan in Group B. In Perth, Greece will face Bulgaria in Group A and France in Group F against Argentina.