Ivanovic had a foot problem, while Petrova was bothered by a neck injury. Both players got treatment during the last tournament on the WTA calendar.
"It was a bit sore, but actually when I was moving it was feeling better," Ivanovic said. "Every time I would sit and then stand up from the bench, that's when it was the sorest."
Ivanovic made a fast start, taking a 4-0 lead. Although Vinci managed to get back to 4-2, the Serbian put away the first set with a powerful forehand.
The former French Open champion broke three times in the second set.
Ivanovic was given one of two wild cards for the tournament, which features the six highest-ranked players who have won a title this season but did not qualify for the WTA Championships.
Peng was given the other wild card but fell to Petrova, who lost her serve four times in the match but managed to break seven times.
Peng had won her two previous matches against Petrova this year.
"Today it was very important for me to win that first set," Petrova said. "I had a little bit of difficulty with the serve, especially in the first set.
"There was something going on with my upper back or neck. The adrenaline kicked in and I started not to think about it much. I started to focus more on the game."