CoCo Vandeweghe got the U.S. off to a winning start on the outdoor green clay in Florida with a 6-1 6-4 result over Marketa Vondrousova, but Siniakova's victory very much keeps alive Czech hopes of a sixth title in seven years.
In Minsk, Belarus and Switzerland were also locked at 1-1.
Aliaksandra Sasnovich of Belarus beat Viktorija Golubic 6-3 5-7 7-5 but world number 22 Timea Bacsinszky of Switzerland levelled the tie with a 6-4 7-5 win over Aryna Sabalenka.
Siniakova was delighted with her performance against Rogers, after converting all five break points that came her way.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"I was just trying to fight every point because I'm a good fighter on the clay so I can play long rallies," she said in a courtside interview with Martina Navratilova, the former champion from her homeland.
Both semi-finals will wrap up on Sunday with the reverse singles and a doubles match.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Clare Fallon)
