The second-ranked Azarenka double-faulted 15 times and was broken five times by Petkovic, who reached the final here in 2011.
"I'm very happy with my performance," Petkovic said. "I was happy with my movement and my serve for the most part, and I managed to get a lot of balls back very deep and very strong. Parts of the match were a really, really good level -- some parts I lost a bit of energy, but overall I'm very happy."
It was the second tournament in row in which Azarenka lost her first match, having been beaten by Venus Williams in Tokyo last week.
"It was an awful match and a very bad performance from me, so there's not much to say about it," Azarenka said. "It happens once, twice a year to every player, and it happened to me today."
Jankovic had lost three of her four previous matches against Pavlyuchenkova and didn't start well in Beijing, but recovered to break her opponent three times in each of the second and third sets.
The 28-year-old Jankovic, who won the title here in 2008, took control of the match as her opponent struggled with her first serves and double-faulted nine times.
Ivanovic defeated Flavia Pennetta 7-6 (9), 6-1 while Jovanovski took just 77 minutes to dispose of Sorana Cirstea 6-3, 6-2.
In the doubles, wildcard entries Serena and Venus Williams wasted chances to win before losing 6-7 (3), 6-4, 11-9 to Liezel Huber and Chan Hao-ching. Serena Williams double-faulted on match point to hand her opponents the win, and then angrily slammed her racket against the court three times before tossing it to the side.