Barbora Krejcikova and Katerina Siniakova sent the Czech Republic into the Billie Jean King semi-finals with a deciding doubles win over the USA.
The seven-time Grand Slam doubles champions beat Danielle Collins and Taylor Townsend 6-3 7-5 to win the tie 2-1 and book a meeting with Canada.
The 11-times champions were joined in the last four by Slovenia, who reached the semi-finals for the first time.
Slovenia lost 2-1 to Kazakhstan but still went through from Group B.
They had the best sets win-loss record of the three teams in their group and advanced to a semi-final against Group D winners Italy.
Four groups of three teams were competing in the Finals of the women's team competition - formerly known as the Fed Cup - in Seville, with only the group winners qualifying for Saturday's semi-finals.
Czechs win battle of the heavyweights
In the winner-takes-all Group A meeting between the competition's two most successful teams, 18-time champions the USA went 1-0 ahead when Collins beat Siniakova 6-3 6-2 in the opening singles.
But the Czechs - who have won six of the past 11 editions - levelled when Wimbledon champion Marketa Vondrousova overwhelmed 2020 Australian Open champion Sofia Kenin 6-1 6-1 in the second singles.
That meant the place in the semi-finals came down to the doubles, where the Czechs were favourites because of their established and successful pairing of Krejcikova and Siniakova, who are the Olympic doubles champions.
They broke early in the opening set to take charge but were then repeatedly pegged back in a nervy second set that featured seven breaks of serve before eventually making their experience count on their first match point.
'It hasn't sunk in' - Slovenia make history
While the Czech Republic are well used to going far in the tournament, Slovenia are celebrating new territory.
They were the lowest ranked of the 12 teams competing in Seville but sprung a surprise in their Group B opener when they beat last year's runners-up Australia to put them on the cusp of the semi-finals.
With other results going in their favour, Slovenia were able to advance despite Friday's 2-1 loss to Kazakhstan because they ended with the best sets win-loss record of the three teams in their group.
They made an emphatic start when Kaja Juvan thrashed Anna Danilina - ranked more than 700 places below her - 6-1 6-0 before Tamara Zidansek took on Yulia Putintseva.
World number 100 Zidansek knew she only needed to win one set to put her team through, which she took 6-2.
Even though she then went on to lose the next set and then retire injured - and her team then lost the doubles to lose the tie 2-1 - Zidansek had done enough to ensure her team would make history.
"For me, it hasn't sunk it," Zidansek said. "Maybe in a week when we all come home, we'll look back at this. Obviously we still have a lot to do. It's not finished yet."
What is the Billie Jean King Cup - and when do GB play?
Twelve nations were taking part in the Finals of the competition, with teams split into four groups in the round-robin stage.
The group winners advanced to Saturday's semi-finals and the champions will be crowned after Sunday's final in Seville.
The winners will receive prize money of $2.4m (£2.1m), which is part of an overall payment pot of $9.6m (£8.4m) - a record figure for the event which matches the cash awarded in the men's equivalent Davis Cup.
Great Britain did not qualify after losing to France in April's qualifying stage, instead going into a play-off tie against Sweden in London on 11-12 November.
Led by Katie Boulter, GB face Sweden at the Copper Box Arena with a place in next year's BJK Cup qualifiers at stake.
The tie, which consists of five matches - four singles contests, with a deciding doubles if needed - will be shown live on BBC Sport.