Wozniacki was at her best during the match, which lasted one hour and 12 minutes, and only committed three unforced errors, while Giorgi made 30.
"It was nice to win this one. You never really feel comfortable against a player like her – she hits the ball as hard as she can," Wozniacki told reporters after her match. "Thankfully for me, her shots weren't really going in that much. I also kept serving well and I returned well, which was a big help for me today."
Wozniacki will now face number 20 seed Garbine Muguruza after she stunned number 10 seed Angelique Kerber 7-6 (12), 1-6, 6-2 in two hours and 34 minutes.
While Muguruza has a 2-1 head to head advantage over Wozniacki, the Dane is confident about her chances of beating the Venezuelan, especially as she triumphed over her 6-4, 2-6, 6-2 in their last meeting in the semi-final of the Toray Pan Pacific Open in Tokyo in September last year.
"I actually haven't watched her play here so far this week, but I've had some tough matches against her in the past," Wozniacki said. "She's a big hitter. She plays really well. It's going to be a difficult one. But I'm excited for the challenge and I'm definitely happy to be in the next round."