The Israeli had never previously taken a set off Wozniacki, the US Open runner-up, in three previous matches, including at last month's Australian Open.
Also, second-seeded Svetlana Kuznetsova was eliminated when she lost to compatriot and qualifier Regina Kulikova 5-7, 7-6 (2), 6-4.
Peer had at least one break opportunity in each of Wozniacki's 10 service games, and closed it out on her fifth match point. Wozniacki, at a career-high No. 3 ranking, held serve only twice.
"She played really well," Wozniacki said. "She kept changing the rhythm all the time. I had a few unforced errors early in the match and never managed to put her under pressure." In reaching at least the quarterfinals for the fourth time in five tournaments this year, Peer was rapt.
"I played very, very good, and I'm really happy," Peer said. "I was dominating from the first game until the end.
"When I played her in Australia, I played well in the first set, and I had my chances but I didn't take them. So I knew the next time I have to play her, I really need to take my chances because she never gives up. She's always there.
I'm really happy I could manage it." Last year, the organizers were fined $300,000 by the WTA for Peer being unable to play in the event after a visa was denied by the United Arab Emirates government, citing security reasons.
Wednesday's match was moved to Court No. 1 at the Aviation Club as it was the most secure, a decision Wozniacki agreed with even though she said the court speed was different.
"If there is a threat to her, there is a threat to me as well," Wozniacki said. "So I completely agree with the fact that the match was scheduled on Court No. 1. I'd rather be safe than sorry." Peer broke decisively to lead 4-1 in the first set. In the second, she missed serving for the match at 5-4, and at 6-5 had to save another break point before finishing off the Dane.
The other matches went as seeded: Fourth-seeded Victoria Azarenka beat Anna-Lena Groenefeld of Germany 6-1, 4-6, 6-3, seventh-seeded Agnieszka Radwanska dispatched Flavia Pennetta of Italy 6-3, 6-0, and eighth-seeded Li Na overcame Marion Bartoli of France 3-6, 7-5, 6-0.
Clijsters gets ready for Serena showdown in NYC
Meantime, Kim Clijsters is expecting a much quieter New York showdown with Serena Williams this time around.
Clijsters will play Williams in the Billie Jean King Cup on March 1 at Madison Square Garden. It's a rematch of the US Open semifinal, which featured Williams' infamous outburst at a line judge and a record $82,500 fine.
"It will be a happy atmosphere on court, not as serious as Grand Slams," Clijsters said Tuesday in a conference call from Bree, Belgium. "You want to win, but it's a little bit more fun."
The exhibition highlights the three Grand Slam winners plus Venus Williams. In the other one-set semifinal, Venus will face French Open champion Svetlana Kuznetsova. The winners will play a best-of-three final for $1.2 million in prize money.
Clijsters called it a "sad" way to end the match against Williams at the US Open in September. Williams was called for a foot fault on a critical serve, then unleashed a profanity-laced tirade at the line judge that cost her a point penalty, which ended the match.
"We both played an extremely good match and it gets overpowered by the ending," Clijsters said. "I hope we can bring the level we both had at US Open at Madison Square Garden. That would be the best thing for both of us."
Clijsters and Serena Williams recently joined forces in an Australian Open exhibition that raised funds for earthquake-hit Haiti.
"We played mixed doubles against each other, sitting together watching the men play and chatting away having some fun conversation on the sideline," Clijsters said.
"It's lucky our (microphones) weren't on," she said, laughing.
Serena Williams picked up her 12th Grand Slam victory at the Australian Open, tying King in the record books. Clijsters is coming off a "frustrating" 6-0, 6-1 loss to Nadia Petrova in the third round.
Clijsters won the US Open in just her third tournament back from retirement. She'll return to New York with her daughter, Jada, who will be celebrating her second birthday.
Clijsters will compete in Madison Square Garden for the first time since the 2000 Chase Championships. The BNP Paribas Showdown for the Billie Jean King Cup is being held at the Garden for the second straight year.
