Lucie Safarova and Petra Kvitova gave holders the Czech Republic a 2-0 lead over France in the Fed Cup semi-finals after the opening rubbers on Saturday.
Russia had the same advantage over Germany in their tie at Sochi.
On the hardcourt of the CEZ Arena in the eastern Czech city of Ostrava, world number 13 and Czech number two Safarova took an hour and 58 minutes to beat 29th-ranked Caroline Garcia 4-6 7-6 (7-1) 6-1.
World number four Kvitova then saw off 58th-ranked Kristina Mladenovic in 6-3 6-4 in an hour and 21 minutes to take the Czechs within a point of the finals.
The two lefties already led the Czechs to Fed Cup titles in 2011 2012 and 2014 while France are playing the first semi-finals since 2007 after winning their last Fed Cup trophy in 2003.
Coming back after a month-long break from the sport, Kvitova, the 2011 and 2014 Wimbledon champion, lacked her usual spirit against the 21-year-old Mladenovic.
But a break in the first set and two in the second were all the 25-year-old Czech needed against an even more lacklustre Mladenovic, preferred by French captain Amelie Mauresmo over a better-placed Alize Cornet for the opening singles.
“It was a tough game, I have come back after a longer pause and I didn’t know what to expect from myself,” said Kvitova.
“I got a boost from the first point won by Lucie, it was a bit easier for me to play.”
In Sunday’s reverse singles, Kvitova is due to face Garcia and Safarova will then take on Mladenovic, but the captains may decide to change the teams.
Czechs Karolina Pliskova and Barbora Strycova were drawn against Alize Cornet and Pauline Parmentier for Sunday’s doubles.
In Sochi, Anastasia Pavlyuchenkova battled back from a set down to defeat Sabine Lisicki 4-6 7-6 (7-4) 6-3 and Svetlana Kuznetsova beat Julia Goerges 6-4 6-4 as four-time champions Russia edged closer towards the final.
The 23-year-old Pavlyuchenkova enjoyed her second win in as many meetings with Lisicki, who is 19th in the WTA rankings.
“I feel worn out but I’m really happy to give my team this win today,” Pavlyuchenkova said of their clay-court battle.
“After winning the second set in the tiebreak I was stoked and it helped me to start the deciding set pretty well.”
Kuznetsova, currently 24th in the WTA rankings, became Russia’s most successful player in Fed Cup history with her 27th win.
“It was a very nervous match as we both wanted to show our best tennis today,” Kuznetsova said.
In Sunday’s reverse singles, Kuznetsova will play Lisicki before Pavlyuchenkova faces Goerges.
In Sunday’s last rubber Elena Vesnina and Vera Zvonareva, a replacement for the injured Maria Sharapova, will play Angelique Kerber and Andrea Petkovic in the doubles.