NEW YORK — Victoria Azarenka needed to win the second set twice. She had plenty left to pull away for a three-set victory at the US Open.
The second-seeded Azarenka took 2 hours, 40 minutes to close out Alize Cornet, 6-7 (7-2), 6-3, 6-2, in the third round Saturday.
Serving on game point at 5-3 in the second, she pumped her fist and started walking off the court after the 26th-seeded Cornet hit a backhand into the net. The chair umpire had to get her attention to inform her that the line judge had called Azarenka’s previous shot out — replays showed it landed inside the baseline.
The umpire overruled the call, but they still had to replay the point. ‘‘Are you freaking kidding me?’’ Azarenka howled to the chair ump. ‘‘What the hell are you doing?’’
On her second try at set point, Azarenka hit a forehand wide to send the game to deuce. But she won the next two points to clinch the game and the set, after all.
Then she dominated the third set to advance to face 13th-seeded Ana Ivanovic, who rallied to beat young American Christina McHale in three sets. Even with McHale’s loss, it’s still been a promising tournament for the generation of US women who must succeed the Williams sisters.
Serena Williams gets a much-anticipated rematch with 20-year-old Sloane Stephens on Sunday. They’re joined in the Round of 16 by a less expected American, wild card Alison Riske.
Former No. 1 Caroline Wozniacki was ousted in the final women’s match of the day, falling, 4-6, 6-4, 6-3, to Camilia Giorgi, a 173d-ranked qualifier. Giorgi hit 46 winners to 13 for Wozniacki, the 2009 runner-up at Flushing Meadows who came in seeded sixth.
Giorgi will play another Italian, No. 10 Roberta Vinci, in the fourth round. This is the Giorgi’s second round-of-16 appearance in a major; she made it that far at Wimbledon last year. The 21-year-old, who won three matches in qualifying to earn a spot in the main draw, is the first woman qualifier to reach the fourth round of the US Open since Anna-Lena Groenefeld in 2008.
Maybe’s Riske’s run isn’t that much of a surprise considering her recent surge. The 23-year-old Pittsburgh native came into the summer having never accomplished any of these feats: winning a match in a Grand Slam tournament, at a WTA Tour event on hard courts, or against a top-10 foe.
She’s now achieved all that, her latest breakthrough victory a rout of 2011 Wimbledon champ Petra Kvitova. Riske won, 6-3, 6-0, taking the last eight games against the seventh-seeded Czech, who was in bed with a fever the day before.
‘‘I’ve got a new confidence in myself,’’ the 81st-ranked Riske said through tears in an on-court interview. ‘‘I believe that I belong here.’’
McHale was one game away from matching Riske in upsetting a former major champion to reach her first Grand Slam fourth round. The 21-year-old had a chance to serve out the match at 5-4 in the second set, but Ivanovic broke back.
The 2008 French Open champ then saved two break points at 5-5, and she broke McHale’s serve in the next game to clinch the second set.
Ivanovic broke McHale again in the final game of the third set for a 4-6, 7-5, 6-4 victory in 2 hours, 26 minutes.
McHale has been ranked as high as 24th, but she’d slipped to No. 114 after a bout with mononucleosis.
‘‘After some of the losses I’ve had this year, even though today it hurts to lose this type of close match, I feel much better about my game,’’ she said.
Riske was 0-5 at major tournaments before Wimbledon this year but is 5-1 since. She just broke into the top 100 in late July; now Riske will likely earn a top-60 ranking. ‘‘It’s really tough out here,’’ she said. ‘‘Every week isn’t like this.’’
She has always thrived on grass, making the third round at Wimbledon this year. Now she’s starting to figure out the hard courts. She next faces an unseeded opponent, Daniela Hantuchova.
Kvitova said she tried to end points quickly, knowing she couldn’t hold up through long rallies. But Riske stayed calm and played good defense, taking advantage of Kvitova’s seven double faults and 27 unforced errors.
‘‘She moved well,’’ Kvitova said. ‘‘She pushed me to the back. That was tough for me.’’
It’s another frustrating finish at Flushing Meadows, the only major tournament at which Kvitova hasn’t made the semifinals. Two years ago, she became the first reigning Wimbledon women’s champion to lose her first US Open match in the same season.
‘‘My body wouldn’t let me fight,’’ Kvitova said.
Saturday opened with two upsets: Simona Halep, seeded 21st, crushed No. 14 Maria Kirilenko, 6-1, 6-0; and Flavia Pennetta beat 27th-seeded Svetlana Kuznetsova, 7-5, 6-1. The two face each other in the fourth round. Halep, 21, extended a sizzling summer with her first trip to a Grand Slam fourth round. She’s coming off a title at New Haven.