NEW YORK—World No. 2 Angelique Kerber took to Louis Armstrong Stadium on Wednesday to take on experienced veteran Mirjana Lucic-Baroni. The German had to fight for it, saving two set points to win, 6-2, 7-6 (7).

“I was feeling very well in the first set,” Kerber said. “…. and the first few games I played well. But I know that she is always fighting until the last point, and she played better and better during the match.”

The German is having the summer of a lifetime, having reached the final of Wimbledon, the gold-medal match at the Olympics and the final in Cincinnati. (Had she beaten Karolina Pliskova in Cincy, she would have supplanted Serena Williams as the world No. 1.) Being back in New York has boosted her confidence level. In 2011, the 28-year-old put the world on notice by reaching the semifinals.

“The Grand Slams are really special, especially this one because everything [started] for me here in 2011,” Kerber said. “It’s great to be back here.”

On Wednesday afternoon, Kerber jumped ahead 2-0 before anyone in the crowd had gotten settled. A long game finally ensued, with Lucic-Baroni able to keep more shots in the court, but the in-form No. 2 seed sealed the game for a 3-0 lead.

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Mirjana Lucic-Baroni far too inconsistent as Angelique Kerber advances to third round of U.S. Open

Mirjana Lucic-Baroni far too inconsistent as Angelique Kerber advances to third round of U.S. Open

Lucic-Baroni, ranked No. 57, beat Alize Cornet handily in the first round. The 34-year-old has had an up-and-down year, highlighted by reaching the Strasbourg final for the second time. (She previously reached the final there in 1997.) She is no stranger to upsets in New York; two years ago, in her best-ever showing at the U.S. Open, she upset Simona Halep to advance to the fourth round.

Lucic-Baroni finally got on the board for 1-4, but there wasn’t much she could do to shake the German’s backboard. Kerber hit just four unforced errors to Lucic-Baroni’s 24. Kerber hit a rare ace to take the first set, 6-2.

Lucic-Baroni’s only hope against Kerber, who was playing incredibly high-percentage tennis, was to take some calculated risks and step into the court. In the second set, her winners (23) began to catch up with her errors (31).

Kerber raced out to a 4-1 lead and appeared to have the match in the bag. But Lucic-Baroni wasn’t fading. The Australian Open champion made a few rare errors at 2-4 to put Lucic-Baroni within one game for the first time. A little momentum was all the Croatian needed to even the match, and her flat, penetrating strokes started doing some damage.

The German’s biggest weaknesses are normally her serve and her attitude, but she stayed composed despite the second-set hiccup.

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Mirjana Lucic-Baroni far too inconsistent as Angelique Kerber advances to third round of U.S. Open

Mirjana Lucic-Baroni far too inconsistent as Angelique Kerber advances to third round of U.S. Open

“I was trying to stay positive and be focused, and [was] fighting until the last point,” Kerber said. “So I’m happy to be in the third round.”

Against Lucic-Baroni, Kerber’s subpar serve didn’t particularly hurt her. The Croat hit seven double faults, and neither player got more than 60 percent of their first serves in.

Still, Lucic-Baroni had the edge throughout the second-set tiebreaker, hitting powerful winners to inch ahead. But, in keeping with the pattern of the match, she followed them up with sloppy errors. The world No. 57 had two chances to push the match to three sets, but her high-risk game failed to pay dividends. Instead, Kerber took advantage of her first match point to win the second set, 7-6 (7).

Kerber will play either Shelby Rogers or CiCi Bellis in the next round.