Bernard Tomic produced a superb display against world number 21 Tommu Haas to win 7-6(6) 3-6 7-5, but Germany looked set to get back on level terms as Petkovic took her opening set against 16-year-old Ashleigh Barty 6-4.
An injury to her right knee ended Petkovic's hopes, however, and Germany were forced to concede both that match and the doubles clash to give Australia a 3-0 win.
“It’s unfortunate for Andrea, she’s a great player,” Barty said.
“I hope Andrea has a speedy recovery so she can play in the Australian Open.”
In the other match of the opening day, Spain enjoyed the narrowest of victories over South Africa as their clash came down to a super tie-break in the doubles.
In the men's singles Kevin Anderson beat Fernando Verdasco 7-6(5) 6-4, but Anabel Medina Garrigues thrashed Chanelle Scheepers 6-4 6-2 to level the scores at 1-1.
Spain won the opening set of the deciding mixed doubles, but Germany took the second on a tie-break to send the match to a super-tie break decider, which saw Spain come through 6-4 6-7(3) 10-8.