SINGAPORE—Caroline Wozniacki has yet to win a Grand Slam, and the former No. 1 has lost to plenty of the world’s Top 10 over the past three years, but the Dane has never given up—and finally has become much more aggressive and sure of herself.

The day before their final round-robin match, Petra Kvitova said that she hadn't played Wozniacki in more than a year and wanted to see whether she could stay with her resurgent opponent. The answer was no, as Wozniacki overwhelmed her powerful adversary, 6-2, 6-3, to clinch a spot in the semifinals.

Wozniacki didn't just hope that Kvitova would miss with her gigantic strokes, she moved forward and dictated play. Wozniacki knows full well of the criticism she’s received during her fall from grace, something she does not appreciate.

“I believe in myself and I believe in my skills,” she said after the match. “I've been playing well, so I believed I could beat anyone.”

Wozniacki has always had her backhand; it's her most powerful shot. But her forehand and serve haven’t measured up. Against Kvitova, however, she struck all her shots deep and into corners. Kvitova tried to dig into the match, but was too inconsistent while Wozniacki was near perfect.

The 24-year-olds have taken different career paths to this point. Wozniacki rose more quickly, reaching a Slam final at the 2009 U.S. Open, while Kvitova needed more time to develop both her strength and speed on court. Wozniacki was tireless and very consistent, while Kvitova was up and down in 2010, when the two met each other three times. Wozniacki bested Kvitova on clay and hard courts, then the two met in a grass for the first time. Right there, in the blink of an eye, it all changed.

They faced off in the round of 16 at Wimbledon, where Kvitova won in a rout, 6-2, 6-0. She nailed winner after winner by hitting as hard as she could; her left-handed forehand bombs were practically untouchable. Even Wozniacki, one of the game's fastest players, wasn’t quick enough to reach Kvitova’s shots.

From there, Kvitova rose to the forefront in 2011, winning Wimbledon while Wozniacki began to slip. At the Australian Open, Wozniacki held a match point before losing to Li Na in the semis. It began an extended loss of confidence and form. Kvitova would win their next three matches before Wozniacki flipped the script last year in Cincinnati, where she prevailed in three sets.

In 2014, while Kvitova collected another Wimbledon title, Wozniacki reemerged within the game’s elite, scoring wins over Top 10 players and reaching the U.S. Open final. It helped earn her the final spot in the WTA Finals, where she outlasted Maria Sharapova, out-stroked Agnieszka Radwanska, and perhaps most impressive of all, ousted Kvitova (the loss eliminated the Czech from contention). After the contest, Kvitova was impressed, saying, “Caro played very relaxed.”

Wozniacki’s next challenge should be her toughest yet: Serena Williams, in Saturday’s semis. The world No. 1 holds a 9-1 record against Wozniacki, including victories in this year’s and the 2009 U.S. Open finals. Regardless, Wozniacki has put together wins against world No. 2 Sharapova, No. 3 Kvitova, and No. 6 Radwanska this week: She is relevant again.

“I never left really,” she said. “I'm just happy to be in the position I'm in now. I never felt I was away.”