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Mertens defeated Giorgi 6-4, 6-2 in one hour and 44 minutes on Wednesday.
"I knew I needed to play a good game to beat her, because she played a couple of good matches last week so she had that kind of rhythm already," Mertens told WTA website.
"But I'm happy with my performance. I knew I had to play more aggressively, because she has those amazing strokes and also some mistakes.
"I had to stay focused to try to play my game and be sometimes more aggressive than her and really take the ball early," she added.
The Belgian will now face the winner of another Round of 16 clash between Tamara Zidansek or wildcard Eugenie Bouchard.
In other second-round match, Kristyna Pliskova delivered the biggest upset of the tournament so far as she ousted No.2 seed Petra Martic 6-1, 7-5 in one hour and 22 minutes.
"I feel I'm playing better on clay each year," Pliskova said afterwards. "Everybody was saying I cannot move and stuff, but I don't think it's like this - I have more time, so it's good for me that clay is not that fast, I can focus on my game," she added.
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