Caroline Wozniacki outlasts Maria Sharapova in humid U.S. Open match

— It is turning out to be the relationship that gives engagements a bad name. First, golf star Rory McIlroy calls off the wedding with tennis star Caroline Wozniacki and wins the British Open and the PGA.

Then, Wozniacki starts a run of success just before Wimbledon at the Eastbourne tournament in England, a span that includes 18 victories in 24 matches, one title (Istanbul) and a boost in her ranking back into the top 10, leading into the U.S. Open.

And now this. In front of a packed house in Arthur Ashe Stadium, on a day so humid New York dry cleaners celebrated in Times Square, Wozniacki outlasted and outgrunted Maria Sharapova.

Sharapova was seeded fifth, five spots better than Wozniacki, and was favored to win not only because she has won five Grand Slam tournaments and a career slam, but because she has been playing effective and determined tennis of late.

But Wozniacki, the Danish star who was No. 1 in the world for much of 2010 and ’11 before her ranking slipped to No. 18 after the 2013 Indian Wells event — her lowest since ’08 — prevailed, 6-4, 2-6, 6-2.

The weather conditions were difficult, to say the least. The WTA tour has a mandatory break after the second set if weather conditions are bad enough to be dangerous to the players’ health. It was used this time.

“It was humid. It was hot,” said Wozniacki, who is training to run the New York Marathon. “I had to change my dress. That rarely happens. I was just soaked.”

Sharapova was asked if training for a marathon might have helped Wozniacki be in the kind of shape it took to win Sunday.

“I can only speak for myself,” she said. “If I was getting ready for a marathon, it wouldn’t help me.”

The closest Wozniacki has come to a major title was 2009, when she lost in the final here to Kim Clijsters. This victory put her in her first Grand Slam quarterfinal since the 2012 Australian.

“I’m serving well, I’m running well,” she said. “I’m staying aggressive when I have to, and I make the right decisions at the right moment. And I enjoy playing.”

The usual thinly veiled Rory question was asked near the end of her news conference, and she replied, “To be honest, I don’t think that’s a relevant question.…What’s happening off the court is not relevant.”

Her quarterfinal opponent will be Sara Errani of Italy, the No. 1 doubles payer in the world, who also carries a No. 13 seeding here. Errani beat the 32-year-old comeback kid, Mirjana Lucic-Baroni, 6-3, 2-6, 6-0.

Despite an hour and a half rain delay, Roger Federer kept rolling along.

The second-seeded superstar began against Spain’s Marcel Granollers like he wasn’t interested. He trailed, 5-2, when the lightning and rain shut down the match. He came back, won another game and lost one — and the set. Then he allowed Granollers one more game in each set and polished off the match in under two hours, 4-6, 6-1, 6-1, 6-1.

“The biggest difference was the wind,” Federer said. “It was quite windy when we got out. When we came back, basically, it was gone. So, obviously was Granollers.

Fourth-seeded David Ferrer of Spain was an upset victim. He went out to Gilles Simon of France, 6-3, 3-6, 6-1, 6-3.

For both players, as it was with Federer, the weather was the issue.

Ferrer acknowledged that the humidity and sun were “not easy” for him.

Added Simon: “I never sweat like this in the last 10 years.”

bill.dwyre@latimes.com