Kvitova beat Jarmila Gajdosova 7-6 (7-2), 6-3 in Saturday's opening match of the best-of-five series and put the Czech ahead 3-0 with a 2-6, 7-6 (7-3), 6-4 decision Sunday over Stosur.
The Czechs are looking to be the first team to win three consecutive Fed Cup titles since Spain in 1993-95. Prior to that, Czechoslovakia won three straight years over 1983-85 and the United States won seven times in 1976-81.
The Czech Republic, in the semifinals for the fifth consecutive year, will go against either Italy or the United States in the April 20-21 Fed Cup semi.
Wins Saturday by Kvitova and Lucie Safarova, who beat Stosur 7-6 (8-6), 7-6 (7-4), had the Czechs up 2-0 in the series.
Stosur didn't face a break point in jumping to a 1-0 set lead versus Kvitova and had a match point at 5-4 of the second but Kvitova saved that and rallied in the tiebreaker. Kvitova built a 5-0 lead in the third set only to have Stosur battle back to 5-4 before Kvitova was able to finish off her sixth break of the match and secure the series.
Stosur was a hard-luck loser in both her matches. She won as many points as Safarova (101-101) Saturday and as many as Kvitova (92-92) Sunday. She had more breaks (seven) than Kvitova, also.
New Fed Cup rules abandoned the meaningless fourth singles match but the Czechs made the official score 4-0 when Andrea Hlavackova and Lucie Hradecka teamed for a 6-0, 7-6 (7-1) win over Ashleigh Barty and Casey Dellacqua in a doubles match.