The top-seeded Wozniacki defeated Hsieh Su-Wei of Taiwan 6-2, 6-2 in 60 minutes while it took Vinci five minutes longer to rout Slovakia's Daniela Hantuchova 6-1, 6-2.
Wozniacki converted all five of her break points and only lost her serve once, in the second set.
"I always try to finish my matches in two sets and I am happy that this time it worked," said Wozniacki, who is coming off titles in Seoul and Moscow. "I will try to finish this season with a hat trick."
The fourth-seeded Vinci dominated throughout, breaking five times. The two traded breaks to start the second set, but the Italian then jumped out to a 4-1 lead to take control.
Wozniacki will play Vinci on Wednesday, with the winner likely clinching a spot in Saturday's semifinals. The first two in each group advance.
In the other group, Bulgaria's Tsvetana Pironkova came from behind to dispatch sixth-seeded Zheng Jie of China 2-6, 6-4, 7-6 (4). Pironkova took a 3-0 lead in the third set before being forced into a tiebreaker.
The Tournament of Champions features the six highest-ranked players who have won a title during the season but did not qualify for the WTA Championships, along with two wild cards.
It is the final event on the WTA calendar.