NEW YORK — Her lead slipping away, her Achilles tendon hurting, Roberta Vinci reminded herself of all the times she celebrated victories at the U.S. Open.

“It helps me in delicate moments,” the 2015 runner-up said Friday after another win at Flushing Meadows.

“In the end, the head does a lot,” she added. “If you think negatively, it’s hard to get out of tense moments. So I try to think about what I did last year, what I’ve done in other years.”

For another past U.S. Open finalist, this tournament is also a rush of positive thoughts. Caroline Wozniacki, a former top-ranked player, had failed to win any matches at the majors this year when she arrived at Flushing Meadows.

Now she’s into the round of 16 — the first time since January she’s posted three victories at the same event.

“It feels like my back garden and everything feels so familiar,” said Wozniacki, whose ranking is down to No. 74 after a string of injuries.

For both women, the U.S. Open has been by far the most successful of the majors. Wozniacki has reached the final twice to go along with two other semifinal appearances; she’s been to the semis only once at the other three Grand Slams combined.

This is the fourth time Vinci has made the round of 16 at the U.S. Open — she’s done it just three times total at the other majors. And last year, she stunned Serena Williams in the semis, thwarting the American’s Grand Slam bid and sending Vinci to her first major final at age 32. Vinci also won a U.S. Open doubles title in 2012 with Sara Errani — on Louis Armstrong Stadium, where she played Friday.

The seventh-seeded Vinci didn’t drop a game in the first set, failed to serve out the match in the second, then hung on in the third, needing nearly two hours to top 102nd-ranked Carina Witthoeft 6-0, 5-7, 6-3.

Wozniacki had an easier time in the third round against the tricky slice forehand of 58th-ranked Monica Niculescu, winning 6-3, 6-1. She believes the combination of the Wilson balls used at the U.S. Open and the speed of the courts is perfect for her game.

“The ball goes through the air very quickly, but the court kind of slows it down a little bit,” she said. “So it fits my game well. I can run a lot of balls down. But at the same time, I can get a lot out of my shots, as well.”

And she enjoys the buzz that ripples through Arthur Ashe Stadium, a sound that can distract other players. Wozniacki won on Ashe on Friday and almost certainly will be back there Sunday against American Madison Keys.

The eighth-seeded Keys leaned on the urging of the home crowd on Ashe on Friday when she rallied from down two breaks in the third set for another great escape. Japanese teenager Naomi Osaka twice served for the match, but Keys got the break both times and went on to win in a third-set tiebreaker 7-5, 4-6, 7-6 (3).

Keys was also two points from defeat in the first round against 60th-ranked Alison Riske. Asked on court if Friday’s win was the best comeback of her career, Keys said: “For sure. Hands down.”

Keys is well aware that Denmark’s Wozniacki, who has an apartment in Manhattan, is a fan favorite at the U.S. Open who will draw plenty of cheers Sunday. Vinci, too, has been wildly popular ever since she charmed the crowd in her on-court interview after last year’s win over Williams.

Vinci was wearing a U.S. Olympic team T-shirt after Friday’s victory. She bought it recently because she thought it looked cool, and the fans in Flushing Meadows would probably agree they consider the Italian a member of the home team.