The Italian defeated the defending champion 6-2 2-6 6-4 to reach the quarter-finals where she will face the former world number one Victoria Azarenka.
"It was a very good match," Giorgi said afterwards. "This is a nice court and (today) was very fun."
Meanwhile, Azarenka had little trouble knocking out the seventh seed Ashleigh Barty 6-4 6-2, saying later: "I think I played a lot better than in the first round. I felt I really controlled today and found the court really well.
"Obviously it's been a while since I've played. I'm just trying to look day by day and see what happens. But I'm definitely enjoying my time on court these days."
Elsewhere, Barbora Strycova edged past Anett Kontaveit 7-5 3-6 7-5 and will face US Open champion Naomi Osaka in the quarter-finals.
Donna Vekic, who knocked Sloane Stephens out in the first round, defeated the out-of-sorts Johanna Konta 6-3 7-5 to set up a quarter-final with Caroline Garcia.
Giorgi is 9/1to win the Pan Pacific Open outright, while Azarenka can be backed at 5/1, Vekic at 9/1andOsaka at 2/1