World number one and defending champion Wozniacki of Denmark posted a 6-3 7-6 (7/3) victory over Estonia's Kaia Kanepi on the hardcourts in Beijing.
Number 13 seed Anastasia Pavlyuchenkova of Russia also progressed to the last eight, but did not have to hit a ball as Belarus' Azarenka withdrew citing a right foot problem.
Next up for Wozniacki will be a quarter-final clash with Italy's Flavia Pennetta, who battled past Slovakia's Dominika Cibulkova 6-1 4-6 6-4, while Pavlyuchenkova will take on ninth-seeded German Andrea Petkovic.
Romania's Monica Niculescu, who ousted French Open champion Li Na earlier this week, came from a set down to overcome French fellow qualifier Virginie Razzano 4-6 6-1 6-2.
Niculescu will face Maria Kirilenko in the last eight after the Russian breezed past Austria's Tamira Paszek 6-1 6-2.
Agnieszka Radwanska, the 11th seed from Poland, also enjoyed a straightforward triumph, 6-4 6-2 against Sweden's Sofia Arvidsson. Her reward will be a last-eight encounter with former world number one Ana Ivanovic of Serbia.
In the second round of the men's event running parallel to the women's tournament, top seed and world number seven Jo-Wilfried Tsonga defeated Chinese wild card Ze Zhang 6-3 6-4 to boost his hopes of reaching November's ATP World Tour Finals in November.
The Frenchman will play Juan Carlos Ferrero in the quarter-finals after his 6-4 6-4 victory over fellow Spaniard Marcel Granollers.
Ferrero told www.atpworldtour.com: "Marcel is a very good friend of mine, so it's always not nice to beat him or another player."
Looking ahead to a clash with Tsonga, Ferrero added: "I think he's a great player. He's in a good shape. He's been playing very well for most of the season on the hard courts, and of course he's one of the favourites to win the tournament.
"But it's going to be a nice match for me. He has beaten me on hard court and I beat him on clay court. It will be another challenge for me."
South Africa's Kevin Anderson progressed by edging two tie-breaks against Spain's Albert Montanes to win 7-6 (7/3) 7-6 (7/4), and will play Marin Cilic in the last eight after the Croatian overcame Italy's Fabio Fognini 6-2 6-7 (7/1) 6-3.