NEW HAVEN, Conn. -- Caroline Wozniacki took some time to reminisce after moving into the semifinals in New Haven for the sixth consecutive year.

"It's unbelievable how the time flies," she said. "I've played a lot of good matches, a lot of tough matches. I've had rain delays. I've played indoors, outdoors in the heat, night sessions. I've played with some wind, with a hurricane coming in. You know, I played with a bit of everything."

The four-time tournament champion beat American Sloane Stephens 7-6 (6), 6-2 on Thursday, improving her record to 23-1 at the Connecticut Tennis Center, with her lone loss coming a year ago when she had to retire from the semifinals because of a knee injury.

"I don't think there's many players that have won an event four times already," she said. "I'm pretty proud of my achievement actually. You know, I think it's pretty impressive."

The former No. 1 player in the world will play Simona Halep on Friday. The Romanian beat Russia's Ekaterina Makarova 6-1, 7-6 (6).

The other semifinal will feature two players from the Czech Republic. Defending champion Petra Kvitova beat Russia's Anastasia Pavlyuchenkova 2-6, 6-2, 7-5. She will face Klara Zakopolova, who came from a set down to beat Russian Elena Vesnina 4-6, 6-0, 6-4.

Stephens, the 20-year-old rising U.S. star, stayed with Wozniacki early and was serving for the set after breaking the Danish star in the ninth game. But Wozniacki broke back to tie the set at 5-5 and never trailed in the tiebreaker, winning 8-6.

Wozniacki broke Stephens in the third game of the second set, and put the match away with another break to go up 5-2.

"We both were playing well," said Stephens, who is still looking for her first WTA tournament title. "It's just unfortunate that I lost the tiebreaker. But I thought we both played really well."

Kvitova needed three sets and a full day to make her return to the semifinals. Rain delayed the start of play in the early matches by more than an hour and a half, and she was forced to sit through a second, hour-long rain delay, during play.

It was the third three-set match of the tournament for the defending New Haven champion, who leads the WTA Tour's top 100 players with 29 this season. She improved to 18-11 in those contests.

"I know I'm playing a lot of three-set matches, that's why I probably know if I lose the first set, still I can go to the third," Kvitova said. "I don't feel like without energy in the third set, so that's good sign, too."

Zakopalova also came from behind to win her quarterfinal, finding her confidence in the second set, which she won in 28 minutes. She was serving for the match at 5-2 before Vesnina rallied, coming within a point of tying the set.

"I was just fighting for every point," Zakopalova said. "In the end I was a little bit more lucky, I think."

Their match and the earlier quarterfinal between Halep and Makarova were forced to the grandstand court by the rain.

Fewer than 20 fans watched as Halep jumped out early, taking the first 6-1 while breaking Makarova's serve four times.

The second rain delay came with the players tied at 1-1 in the second, and when play resumed Makarova made a run, winning the next two games.

"I was a little bit nervous after (the rain)," Halep said. "I played really slow after. But I came back from 4-2 again and I did well."

The Romanian broke serve in the eighth game, and won the tiebreaker 8-6.

She is looking for her fourth tournament title this summer and said she likes where her game is heading into next week's U.S. Open.

"I'm a bit tired right now," she said. "But I want to play tomorrow, to try my best. After that I will see what will happen."

This is the first quarterfinal in the tournament's history that didn't include either of the top two seeds. Sara Errani and Angelique Kerber both lost earlier in the week in the second round. Kvitova, Wozniacki and Stephens were the only seeded players to make it past round two.

The players got a little excitement before play began Thursday.

A fire alarm, caused by smoke from someone cooking in the players' lounge, forced the evacuation of the Connecticut Tennis Center for about 15 minutes.

"It was OK, when we were waiting for the match, some fun," Kvitova said. "I wasn't cooking, so that's good."