Richard Gasquet reaches quarters
The Frenchman, who won the event in 2005 and 2006 when it was held in Nottingham, has struggled with a back injury and is playing only his third tournament since losing to Roger Federer in Miami in March.
After missing the entire clay-court season leading into Roland Garros, he reached the third round in Paris before losing his opening match on grass last week in Halle.
Tomic threatened by firing 16 aces, but he converted just one of 10 break points.
"I played well out there," Wozniacki said. "Sloane, especially in the second set, played really, really well, and really went for her shots. Didn't make it easy for me to finish it off. I held my composure and I served well. I got a lot of returns deep."
Fifth-seeded Angelique Kerber of Germany saved two match points to overcome Alize Cornet of France 7-5, 1-6, 7-6 (3) in 2 hours, 26 minutes, and Camila Giorgi of Italy struggled to follow up her defeat of former No. 1 Victoria Azarenka, taking just 10 minutes less and saving a match point to defeat British wild card Johanna Konta 1-6, 7-5, 7-5.