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Caroline Wozniacki flipped the script on the traditional post-match press conference in her last presser, offering answers to questions she’s confronted at nearly every Q&A since she attained the top spot.

The world No. 1 didn’t make a strong opening statement today—Anastasija Sevastova, the 46th-ranked Latvian, had a 3-1 first-set lead and broke for 4-all in the second—but Wozniacki had the final word, posting a 6-3, 6-4 victory to advance to the Australian Open quarterfinals for the first time.

While Wozniacki has not surrendered a set in her four tournament wins, she’s relied primarily on her quick counter-punching style and the tactical theory that more points are lost than won, and that virtually no ball is beyond her reach. It’s a high-percentage style that has helped carry Wozniacki to the top of tennis, but will it be enough to propel her to her first Grand Slam title?

She figures to face a significant challenge next in either two-time Grand Slam winner Svetlana Kuznetsova, who just swept finalist Justine Henin in straight sets, or reigning Roland Garros champion Francesca Schiavone. Wozniacki has won three of five meetings with Kuznetsova, including a dramatic 2-6, 7-6 (5), 7-6 (3) triumph at the 2009 U.S. Open. She has split four meetings with Schiavone, winning both of their hard-court clashes last season.

Typically strong out of the starting blocks, Wozniacki stutter-stepped at the start today. She double-faulted to drop serve in the opening game and was victimized by Sevastova’s ability to drive the ball down the line, as the 20-year-old leaped out to a 3-1 lead.

Sevastova’s ability to alter pace—she used her slice backhand effectively and once even tossed in a stretch-slice forehand—and her all-court comfort almost qualifies her for honorary Maleeva sister status. When she’s playing well. But a mind-numbing propensity to overplay the drop shot—against one of quickest players in the sport—and Wozniacki’s accuracy from the baseline contributed to Sevastova’s first-set collapse, as she dropped five consecutive games to lose the opening set.

The pivotal point of the set came in the sixth and seventh games. Taking advantage of two double-faults, Wozniacki swooped forward and flicked a forehand winner to break for 3-all. The 20-year-old Dane then erased two break points and held for 4-3 when Sevastova bunted a forehand volley into net.

Though she had lost in the opening round in five of her seven prior major appearances, Sevastova showed no shortage of self-belief, fighting back from a 2-4 second-set deficit by jabbing at the Wozniacki forehand, as if picking away at a scab, until Wozniacki bled successive errors. It got Sevastova the break for 4-all. But inexperience, increasingly heavy legs and lungs, and Wozniacki’s unerring consistency all conspired against Sevastova in the final two games.

Holding a 40-15 lead, Sevastova hit yet another abysmal drop shot, followed by a tame lob, and wound up losing the point. At 40-30, she was in position for an overhead at net, but the leg-weary Latvian did not do enough with her smash down the center and couldn’t handle Wozniacki’s low reply, netting a volley. Looking frustrated by missed opportunities and fatigued from physically demanding points, Sevastova badly bungled a backhand and dropped serve to hand Wozniacki the break and  a 5-4 lead. Wozniacki wrapped up the win in one hour and 20 minutes, committing just 14 unforced errors compared to her opponent’s 36.

Growing up, Wozniacki looked up to five-time Grand Slam champion Martina Hingis, who played tennis as if it were a physical game of chess—by exploring all areas of the court and working short, sharp angles, as well as depth. Wozniacki said she tries to play the type of thoughtful tennis Hingis played at her best, and thinks of constructing points with clusters of combinations, rather than loading up for low-risk winners.

“Well, for me it's just about being smart. I mean, there's no sense going for the winners if there is no chance to go for the winner,” Wozniacki said. “I play well from the baseline, I set up my shots to get a short ball, and then I go for the winner when I have the possibility.”

Will that answer be enough in her quest to claim her first major title? We'll find out.

—Richard Pagliaro