But the 33-year-old American overcame 34 unforced errors and 10 double faults, improving to 50-2 on the year and sustaining her march toward history.

“I just kept fighting for each point, not for a lot but just one at a time,” Williams said.

“I had been pretty relaxed. Today I was a little tight. I think it showed. Hopefully I can get back to where I was before.”

Williams is trying to complete the first calendar grand slam since Steffi Graf 27 years ago and equal Graf’s open era record of 22 slam singles titles, two shy of Australian Margaret Court’s all-time record.

Williams completed her second “Serena Slam” of four major wins in a row by winning the Wimbledon crown in July and the 33-year-old American can extend her mark as the oldest woman Slam champion.

Bertens was aggressive early, breaking for a 2-1 lead on a running forehand winner, and Williams was off from the start, breaking back to level the first set 5-5 but then double faulting four times before holding on the way to the tie-breaker.

Bertens jumped ahead 4-0 in the tie-breaker but surrendered the next five points on unforced errors and eventually handed the set to Williams, who broke three times in the second set to seal the hard-fought win.

“It definitely doesn’t worry me, being down a lot,” Williams said. “I know I can make a comeback, make a run for it.”

But her form was so shocking that Williams ran to the practice courts to work on serves for more than an hour.

Next up for Williams will be fellow American Bethanie Mattek-Sands, who beat compatriot CoCo Vandeweghe 6-2, 6-1.

“I’ll have to play a little better if I want to win,” Williams said.

Spanish eighth seed Rafael Nadal, a 14-time grand slam champion, ousted Argentina’s Diego Schwartzman 7-6 (7-5), 6-3, 7-5.

“Happy to be through,” Nadal said. “Was a tough battle. I feel lucky to be through.”

Nadal was down 5-4 in the tie-breaker before battling back, saying, “That was the key almost of the match. To take that first set was very important to me.”

Nadal, the 2010 and 2013 US Open champion who missed last year’s event with an injury, improved to 22-1 in past 23 US Open matches after missing 2012 and 2014 due to injury and finishing as the 2011 runner-up.

On a quarter-final collision course with Nadal is top-ranked Novak Djokovic, the reigning Wimbledon and Australian Open champion who attempts to take another step toward his fifth US Open final in six tries later versus Austrian Andreas Haider-Maurer.

Defending champion Marin Cilic and seventh seed David Ferrer advanced nearer a fourth-round meeting.

Croatian ninth seed Cilic fired 19 aces and advanced to the third round by defeating 139th-ranked Russian qualifier Evgeny Donskoy 6-2, 6-3, 7-5.

“It’s sort of unreal. I was working all my life to win a grand slam and now I’m working to defend one,” Cilic said.

Spain’s Ferrer, the 2013 French Open runner-up who missed the past 2 1/2 months with an elbow injury, downed 102nd-ranked Serb Filip Krajinovic 7-5, 7-5, 7-6 (7-4).

“I’m very happy I’m in the third round,” said Ferrer. “It’s a nice comeback playing on these courts.”

Williams could reach a grand slam singles final without facing a top-10 rival for the first time in her career.

Swiss teen Belinda Bencic, the highest seed remaining in Williams’ half of the draw at 12, faced Japan’s 88th-ranked Misaki Doi later.

Bencic, who defeated Williams in the Toronto semi-finals last month, could play Serena’s older sister, Venus, who meets fellow American Irina Falconi later, in the third round.

Either Bencic, 18, or Venus, 35, could meet Serena in the quarter-finals.

Australian Open semi-finalist Madison Keys ripped 100th-ranked Czech Tereza Smitkova 6-1, 6-2. The American 19th seed hopes for a fourth-round date with Serena Williams, who ousted her in Australia.

“Fingers crossed it could happen. If it does happen I could come out and have some fun at my home Slam,” Keys said.

Canadian 25th seed Eugenie Bouchard advanced over Slovenia’s Polona Hercog 6-3, 6-7 (2-7), 6-3, to reach round three. She had not won back-to-back matches since March.

“She was tough getting balls back but I held my nerve at the end which I thought was the key to the match. I’m excited to win two matches in a row.”