Wozniacki, the top seed, defeated fifth-seeded Hsieh Su-Wei 6-2, 6-2 and the fourth-seeded Vinci was a 6-1, 6-2 winner over No. 7 Daniela Hantuchova in the first Group Serdika matches of the tournament.
Wozniacki dispatched Hsieh in 60 minutes by going 5-for-5 in converting break chances. Hsieh managed one break but Wozniacki lost only 16 points over eight games serving.
Vinci's rout of Hantuchova took just 65 minutes. She won two-thirds of the points on serve, dropping serve once, and 60 percent when receiving. Vinci finished off five of her eight break point opportunities.
Wozniacki is to go against Vinci Wednesday with the winner taking a big step toward qualifying for Saturday's semifinals. The top two finishers in each group advance.
Eighth-seeded Tsvetana Pironkova held on for a 2-6, 6-4, 7-6 (7-4) decision over sixth-seeded Zheng Jie n Group Sredets. Pironkova led 3-0 with two breaks in hand in the third set but Zheng forced a tiebreaker only to have Pironkova eke out the win.
Wednesday's schedule calls for a pair of Group Sredets matches as Zheng goes against second-seeded Nadia Petrova and Pironkova meets No. 3-seeded Maria Kirilenko in addition to the Wozniacki-Vinci Group Serdika match.
The Tournament of Champions is an eight-player event with invitations extended to the eight highest-ranked winners of WTA tournaments in 2012 who didn't play in last week's WTA Championships.
The groups are named for areas in Sofia.