PARIS — Serena Williams’s chest was heaving between points. Her footwork wasn’t quite right. Miscue followed miscue, until she was a set and a break down in the French Open quarterfinals.
And as she so often does, Williams came through when she needed to, moving closer to a record-equaling 22d Grand Slam title by figuring out a way to beat Yulia Putintseva, 5-7, 6-4, 6-1, on Thursday.
‘‘I kept missing. Just misfiring. Honestly, at one point I didn’t see the light at the end of the tunnel,’’ the defending champion said.
How close was she to her earliest exit at a major since Wimbledon in 2014? Putintseva, who is from Kazakhstan and ranked only 60th, twice was a point from serving for the biggest victory of her career.
‘‘I honestly didn’t think I was going to win that in the second set,’’ said Williams, who will face another unseeded opponent, 58th-ranked Kiki Bertens of the Netherlands, in the semifinals. ‘‘Somehow I did.’’
Williams overcame not only a relentless competitor in Putintseva but also her own shakiness on a day that included a brief rain delay.
And Williams must put in more work Friday against Bertens, who like Putintseva has a tendency to extend points.
There is no rest for the weary at this wet-as-can-be French Open. If Williams gets to Saturday’s final, it will be her fourth consecutive day of play. The top-seeded man, Novak Djokovic, already will reach that total when he meets No. 13 Dominic Thiem in their semifinal.
‘‘The way that the schedule has been going on in the second week,’’ Djokovic said, ‘‘[there] is not much time to really reflect on what you have done.’’
The other men’s semifinal is Andy Murray against defending champion Stan Wawrinka. Their quarterfinals were Wednesday.
Djokovic beat Tomas Berdych, 6-3, 7-5, 6-3, while Thiem eliminated David Goffin, 4-6, 7-6 (9-7), 6-4, 6-1.
Williams got so desperate at one point that she shifted her racket to her left hand — and whiffed. At the end of the first set, Williams had made 24 unforced errors to Putintseva’s two, which seems like it might be a typo but isn't. Still, Williams reached her 31st major semifinal.
Bertens became the first Dutch woman to get that far at a Slam since 1977, beating Timea Bacsinszky, 7-5, 6-2,
‘‘Mentally I feel pretty good. But physically, yeah, it was tough today out there,’’ Bertens said, mentioning a calf problem.
Since Williams earned her fourth consecutive major championship at Wimbledon a year ago for No. 21 overall, she has been beaten in the semifinals of the US Open by Roberta Vinci and in the final of the Australian Open by Angelique Kerber.
This setback would have come against a more unheralded opponent. Putintseva is 21, 13 years younger than Williams, and had never been past the third round at a major.
Yet Putintseva scrambled to nearly every ball and threw her 5-foot-4-inch frame into deep groundstrokes. The turning point came at 4-all in the second set, when Putintseva held two break points. Convert either, and she'd be ahead, 5-4, and serve for the match.
Couldn’t do it.
‘‘The match was very close — and very far — from being on my side,’’ Putintseva said.
When Williams wound up holding with a drop volley winner, she looked up to the gray sky, as if to say, ‘‘Whew!’’
Williams then broke to take the set. Putintseva dropped her racket and shoved the brim of her white cap over her eyes. They would go on to play another 32 minutes, but that was pretty much that.
‘‘I definitely knew I needed to do something different if I was going to stay in the tournament,’’ Williams said. ‘‘I always try to have a Plan B and C.”