Kazakhstan reduced the Czech Republic's lead to 2-1 after Yuriy Schukin and Andrey Golubev beat Radek Stepanek and Jan Hajek in their Davis cup quarter-final in Astans.
The reigning champions - without their two top seeds Tomas Berdych and Radek Stepanek - took a 2-0 lead on Friday thanks to wins for Jan Hajek and Lukas Rosol.
But the hosts fought back in the doubles on Saturday as the Kazakh pair secured a 7-6 (7-2) 6-4 6-3 victory to the delight of the home support.
After rallying from a break down to win the first set, the home duo broke decisively in the ninth game of the second against Stepanek and Hajek, who were playing together for the first time.
They then won the next three games to take a 2-0 lead in the third set and Schukin and Golubev closed it out on their first match point, breaking Stepanek's serve after two hours and 20 minutes of action.
The reverse singles will be held Sunday as the visitors will look to avoid an upset against Kazakhstan, who were the last team to beat them in 2011. Lukas Rosol faces Mikhail Kukushkin, before Hajek meets Golubev.
The winner of the best-of-five series will face either France or Argentina in the last four in September.
That match sees Argentina hold a 2-1 advantage after they won Saturday's doubles match.
David Nalbandian and Horacio Zeballos beat Julien Benneteau and Michael Llodra 3-6 7-6 7-5 6-3 after a remarkable comeback from 4-1 down in the third set.
Zeballos, who had a poor opening set, lifted his game to complement experienced Davis Cup campaigner Nalbandian and stun the French pair who won only three of the last 14 games in windy conditions.
Serbia are also closing in on the semi-finals after Ilija Bozoljac and Nenad Zimonjic won a marathon doubles match to shock the top-seeded pair in the world Mike and Bob Bryan to put the visitors 2-1 ahead.
The home crowd were stunned as the Serbian pair outlasted the Bryan brothers 7-6 (7/5) 7-6 (7/1) 5-7 4-6 15-13 after four hours and 23 minutes of hard-hitting tennis.
World number one Novak Djokovic will attempt to convert Serbia's 2-1 lead in the match to victory when he takes on Sam Querrey in the first billed singles on Sunday at the Taco Bell Arena in Idaho.
The winners will face either Italy or Canada - who also lead 2-1 after another marathon doubles match in which Daniel Nestor and Vasek Pospisil outlasted Italy's Fabio Fognini and Daniele Bracciali 6-3, 6-4, 3-6, 3-6, 15-13.