The 18-year-old Briton, who was the top seed at a WTA event for the first time, held serve in the opening game but lost the next six, while winning just two points on 106th-ranked Wang's serve.
Raducanu, who struggled with a hamstring injury later in the contest, lost a 4-2 lead in the second set but won it in the tiebreaker. She took a medical timeout before saving two match points on Wang's serve at 5-4 in the third but the qualifier broke Raducanu again and closed out the win in her next service game.
Wang next plays Alison Riske, who defeated eighth-seeded American Alizé Cornet 6-4, 6-4.
After the match, Raducanu confirmed Torben Beltz as her new coach following a search to replace Andrew Richardson, who led her to win the US Open in September.
Beltz, 44, previously worked with Angelique Kerber when she won both the US Open and Australian Open in 2016.
"It's obviously a great privilege to be working with such an experienced coach -- I'm definitely very excited to work with him throughout the pre-season and into next year," Raducanu said.
"Things are looking up, it's a very positive feeling and I'm excited about all the work that is to come."
Second-seeded Simona Halep reached the quarterfinal after beating Aliaksandra Sasnovich of Belarus 7-5, 6-3, and third-seeded Danielle Collins of the United States eased past Greet Minnen of Belgium 6-1, 6-2.
Information from the Associated Press contributed to this report.