Rosol, who also had a four-set singles win Friday, defeated Evgeny Korolev 7-6 (7-5), 6-7 (2-7), 7-6 (7-5), 6-2. That put the Czechs, who last year won their first Davis Cup title since 1980 when they were part of Czechoslovakia, up 3-1 in the best-of-five series. The fifth match wasn't played.
The Czechs will go against either Argentina or France in the semifinals Sept. 13-15. Argentina was up 2-1 in that series going into Sunday's matches.
After a first set in which there were no breaks, Korolev evened things by taking the second-set tiebreaker and was up an early break in the third set. But Rosol broke back and took another tight tiebreaker.
That seemed to give Rosol a boost and he raced through the fourth set in 38 minutes, dropping only four points on serve and finishing off both of his break chances in securing the series.
Rosol and Jan Hajek both won singles matches Friday for a 2-0 Czech Republic lead but Andrey Golubev and Yuriy Schukin won Saturday's doubles match in straight set to keep the Kazakhs' chances alive.