Vandeweghe overcame a slow start and two service breaks in the first set, recovering to finish with six aces and converting five of her eight break-point chances in the Bougainvillea group.
"I wasn't really making good contact with the ball, wasn't really making enough balls in court, and I was just very sloppy at the start," Vandeweghe said. "That allowed her to start well into the match, and I just had to keep fighting my way back."
Seventh-seeded Julia Goerges beat No. 10 Magdalena Rybarakova 6-1, 7-6 (5) in the Azalea group, while fourth-seeded Anastasia Pavlyuchenkova defeated Angelique Kerber 6-3, 3-6, 6-2 in the Rose group.
The tournament features the leading players on the women's tour who didn't qualify for the WTA Finals in Singapore last week, in addition to the wild card awarded to Peng. The 12 players are divided into four groups of three.