Barbora Krejcikova and Katerina Siniakova won the decisive doubles rubber against the United States to seal Friday's tie and claim the last place in the Billie Jean King Cup semi-finals.
Krejcikova and Siniakova beat Danielle Collins and Taylor Townsend 6-3, 7-5 to secure top spot in Group A and set up a showdown with Canada in Seville on Saturday for a spot in the final.
"I was very happy when we sealed the winning point today. It was a really good match and I was really excited and happy that we finished it and with the way we played," said Siniakova.
"It's tough to be unbeatable because it's impossible, but I'm proud of how we play and how long we are playing, because it's not easy," said Siniakova of her partnership with Krejcikova.
The pair have combined to win seven Grand Slam doubles titles and Olympic gold in Tokyo.
"Everyone wants to beat us, and they are coming and trying to find things," added Siniakova.
Collins gave the USA -- the record 18-time winners -- the ideal start with a 6-3 6-3 victory over Siniakova, but Wimbledon champion Marketa Vondrousova thrashed Sofia Kenin 6-1, 6-1 in the second singles.
"The US were there, just waiting for the winning moment. It got to the wire and it could have gone either way, but we have a world-class doubles team," said Czech captain Petr Pala.
The Czechs are bidding for a 12th title and first since 2018, the last in a run of six in eight years.
Their rivals Canada are appearing in the semi-finals for the first time since 1988.
- Slovenia move on -
Earlier on Friday, Kaja Juvan helped Slovenia seal their berth in the last four with a straight-sets demolition of Kazakhstan's Anna Danilina.
Juvan, ranked 104 in the world, crushed 814th-ranked Danilina 6-1, 6-0 in 53 minutes.
Teammate Tamara Zidansek won the first set of the second rubber against Yulia Putintseva to ensure Slovenia finished top of Group B and join Italy and Canada in the semi-finals of the women's team event.
Zidansek bagged the first set 6-2 but lost the second by the same score before she pulled out, safe in the knowledge it was enough for Slovenia to progress.
Kazakhstan won the doubles and the tie 2-1, but it will be the Slovenians who meet Italy on Saturday. The Italians qualified on Thursday by finishing first in Group D.
France beat Germany 3-0 in a dead rubber on Friday to take second in the section, while Spain edged Poland 2-1 to finish behind Group C winners Canada.
Clara Burel put France on the right track by beating Jule Niemeier 6-4, 6-3.
Then newcomer Varvara Gracheva won the second singles rubber after German rival Tatjana Maria retired while leading 3-0.
Caroline Garcia and Kristina Mladenovic defeated Niemeier and Laura Siegemund in the doubles.
Poland lost both their ties without Iga Swiatek, who won the WTA Finals at the start of the week to cement her return to world number one.
Rebeka Masarova beat Katarzyna Kawa in three sets before Sara Sorribes Tormo defeated Magda Linette. Poland then won the concluding doubles.
The 2022 edition was won by Switzerland, who beat Australia, but both nations were eliminated in the group stage this year.