The Australian Open champion, who has aspirations of becoming world No.1 again if she can better Simona Halep’s result, trailed her creative opponent by four games to two in the decider before reeling off four games in succession to seal victory.
“She [Barty] played extremely well, I thought,” admitted Wozniacki. “She wasn't making any errors at one point. I think it kind of turned around when I got that net-cord. It went over, and instead of being 5-2 for her in the third [set], I still had a chance to kind of survive.
“I think that's where it changed a little bit. I just kind of stayed in it, and then I served pretty well to close it off.”
Maria Sharapova’s encouraging start to the tournament continued with a 7-5 6-1 triumph over Irina-Camelia Begu. The Russian will encounter Kristina Mladenovic next, who defeated Shuai Zhang 6-4 4-6 6-3.
“It was a lot of hard work,” the five-time Grand Slam champion told the WTA website. “Obviously being down a break to start off both of those sets didn't make things easy for me.
“Although I didn't play at my best level in the first set, I pulled it through. I played some really tough points. I hung in there especially in that final game. Then I really set up a good opportunity for me to step up.”
Elsewhere on the grounds, Carolina Garcia overcame Petra Martic 6-3 7-5, Kiki Bertens brushed past Anastasija Sevastova 6-1 6-4 and Julia Goerges came from behind to dismiss Lara Arruabarrena 2-6 6-4 6-2.