Petkovic opened with a 6-1, 7-6 (7) win over Samantha Stosur while top-ranked German player Kerber had little difficulty beating Casey Dellacqua 6-1, 6-0 in 51 minutes on outdoor hard courts at Pat Rafter Arena.
The reverse singles will be played Sunday, followed by doubles.
Germany is trying to reach its first Fed Cup final since 1992, when it beat Spain for the title.
Ashleigh Barty and Dellacqua, who reached three Grand Slam doubles finals last year, are expected to play doubles for Australia. But unless Stosur and Dellacqua can win their singles matches, the doubles match will be meaningless.
"I was kind of nervous but I just got through it," Petkovic said.
Stosur once again had difficulty playing before her home crowd, where she admits she feels extra pressure. But the 2011 U.S. Open champion and 2010 French Open finalist is having a tough time everywhere this year, making it past the third round at only one tournament.
Unforced errors by Stosur handed Petkovic the first set, but the Australian led 5-3 in the second before allowing the German player to level at 6-6. In the tiebreaker, Petkovic had three match points at 6-3 but Stosur fought off those and another before Petkovic clinched it.
Two years ago, Australia upset Germany 3-2 in Stuttgart in a World Group encounter in which Stosur won both her singles matches.
It is Australia's first semifinal appearance since 1993, and now against heavy odds, the country is trying to win the Fed Cup for the first time since 1974, when seven-time Grand Slam singles champion Evonne Goolagone led Australia to victory.
The Czech Republic and Italy are playing in the other semifinal this weekend. The final is Nov. 8-9.