Osaka had been close to tears during the second set and threw her racquet, before recovering her poise. Osaka faces Latvia's unseeded Anastasija Sevastova in Saturday's semi-finals on Beijing's outdoor hard courts.
"I was sort of apologising for my behaviour because I was kind of stressed", Osaka said when asked what the pair spoke about at the net following the match.
Osaka, who was attempting to reach a third straight final after NY and Tokyo's Pan Pacific Open, was unhappy with her behaviour in Friday's quarter-final victory over Zhang Shuai.
The first of Wozniacki's 30 titles on the WTA Tour came in Beijing in 2010 and she did not drop a single set en route to her third championship of the season.
"I feel great being here. I'm just thinking one match at a time, and it can only get harder from here", said Osaka, who cried following her U.S. Open win that was overshadowed by Serena Williams' altercation with umpire Carlos Ramos.
The Dane, who did not drop a set throughout the tournament, hit 12 winners and won four out of eight break point chances to beat the unseeded Sevastova in 87 minutes.
"Unfortunately, I have been playing through pain in my back this whole week and the doctors have advised me that I need to rest to ensure the injury is not further aggravated and become more serious", she added.
In the men's final, Juan Martin del Potro faced Nikoloz Basilashvili of Georgia.