Wozniacki, 27, had to overcome an inconsistent start, where she lost her opening service game, to beat her Italian opponent in one hour and 16 minutes.
In the end it was a comprehensive win, breaking her opponent’s serve on six occasions.
“I'm happy to be on this surface, happy to be playing here,” said world No.2 Wozniacki. “I think it also helps that centre court here is so nice and so cozy. To have the crowd so close, it feels great. I feel very at home.
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“I'm just happy to get myself tested on the grass this week, and this one was a great test for me, a great one leading up to Wimbledon.”
Elsewhere, Kristina Mladenovic came from behind to beat Heather Watson 6(2)-7 7-5 6-3.
World number 59 Watson took the first set on a tie-break having led 5-2 at one point but 25-year-old Mladenovic claimed the second with a decisive break of serve in the 12th game of a fraught affair.
Buoyed with momentum, Mladenovic took the final set courtesy of its only break, which game in the sixth game to win in two hours and 43 minutes.


Aleksandra Krunic (SRB) beat Andrea Sestini Hlavackova 7-5 6-3 (CZE)
Su-Wei Hsieh (TPE) beat Natalia Vikhlyantseva 7-6(4) 6-2 (RUS)
Kristina Mladenovic (FRA) beat Heather Watson (GBR) 6-7(2) 7-5 6-3
Dominika Cibulkova (SVK) beat Ekaterina Makarova (RUS) 7-5 6-4
Harriet Dart (GBR) beat Kristyna Pliskova (CZE) 7-5 3-6 6-3
Alison Van Uytvanck (BEL) beat Samantha Stosur (AUS) 5-7 7-6(3) 6-3
Kaia Kanepi (EST) beat Kurumi Nara (JPN) 6-2 6-4
Mihaela Buzarnescu (ROU) beat Shuai Peng (CHN) 5-7 6-2 6-1
Agnieszka Radwanska (POL) beat Timea Babos (HUN) 6-3 6-1
Aryna Sabalenka (BLR) beat Sachia Vickery (USA) 4-6 6-0 6-1
1-Caroline Wozniacki (DEN) beat Camila Giorgi (ITA) 6-2 6-3
2-Karolina Pliskova (CZE) beat Anastasia Pavlyuchenkova 6-4 2-6 6-3 (RUS)
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Kenin and Garcia deserve respect for finding strength to split from father-coaches
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