How close was Williams to her earliest exit at a Grand Slam tournament 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.
"She played unbelievable. And 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."
Bertens beat eighth-seeded Timea Bacsinszky 7-5, 6-2.
According to ESPN Stats & Information, it was the 36th time -- the most since 1968 -- that Williams dropped the first set of a match in a Grand Slam event only to rally and win. Chris Event is second on that list with 28 victories after losing the first set and then winning a match.
Williams came through, as she so often does, overcoming not only a relentless competitor in Putintseva but also her own shakiness on a cloudy, chilly day that included a brief rain delay in the third game. The No. 1-seeded American's strokes were off and her range was wrong, to the tune of mistake after mistake after mistake.
She made 11 unforced errors before Putintseva committed one, and at the end of the first set, the count was 24-2. Williams got so desperate at one point that she shifted her racket to her left hand to try a shot that way -- and whiffed.
By the end, the unforced-error statistics read this way: Williams 43, Putintseva 16.
But by the end, too, Williams was asserting herself as no one else currently on tour can, winding up with twice as many winners as Putintseva, 36-18.
"I thought, I just can't go out in straight sets," Williams said in her postmatch interview. "So I just thought if I could just win a set ... At that point, I wasn't playing my best, but she was just playing some different tennis and I just wasn't used to it.
"I had to get into that rhythm, and once I found it, I found my game."
Now Williams can continue her quest for a 22nd Grand Slam title, which would equal Steffi Graf's Open-era record.
Since getting No. 21 at Wimbledon a year ago for her fourth consecutive major championship, Williams has bowed out in the semifinals of the US Open last September against Roberta Vinci of Italy -- ending the American's bid for a calendar-year Grand Slam -- and in the final of the Australian Open this past January against Angelique Kerber of Germany.
This setback would have come in the quarterfinals, though, and against a more unheralded opponent. Putintseva is only 21, 13 years younger than Williams, and had never been past the third round of any major tournament until this one.
Yet Putintseva -- who used to train with Williams' coach, Patrick Mouratoglou -- threw her 5-foot-4 frame into groundstrokes to send balls deep into the court and make things rather interesting for two sets.
At 5-all in the first, Williams went ahead 40-love on her serve, only to get broken. Putintseva then served out that set at love when Williams flubbed a backhand. Putintseva yelled with joy and waved her arms, telling the spectators to rejoice with her, before sitting on the sideline with a wide smile on her face.
Williams hadn't lost a set in the tournament until this match, and this was more like a year ago at Roland Garros, where she was forced to win five three-setters on the way to the championship.
At 4-all in the second set, Putintseva held two break points: Had she converted either, she would have been ahead 5-4 and served for the match. She couldn't do it.
And after holding with a drop volley winner, Williams looked up to the gray sky with her palms aloft.
Williams then broke to take the set when Putintseva double-faulted. Putintseva twirled her racket and dropped it 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.
The third set was lopsided as can be, and when Williams smacked one return winner, she raised her left fist in the air.
Bertens is deep into unchartered territory. Before this French Open, just once in 15 previous Grand Slam tournaments did she advance beyond the second round -- making the fourth round at Roland Garros in 2014.
Bacsinszky is the fourth seeded player to fall to Bertens' march to the semifinals.
After winning the first set, Bertens got treatment on her left calf, which was taped from the start of the match on a near-deserted Court Suzanne Lenglen. She gave a happy thumbs up as the trainer wrapped the muscle in a bandage. The niggle didn't appear to affect her play or mobility.
In the final quarterfinal match, Bertens immediately broke Bacsinszky to jump to a 2-0 second-set lead. Her Swiss opponent grappled with mounting frustration, muttering to herself between points.
On her next service game, Bacsinszky hit a backland long on breakpoint to increase Bertens' lead to 4-0. Bacsinszky then got a break back and held serve to recover to 2-4.
But Bertens saved three break points in the seventh game to take a 5-2 lead. She hit a crisp backhand winner on her second match point for the victory.
Information from ESPN Stats & Information and The Associated Press was used in this report.
Serena survives test from Putintseva to reach semis
Defending champion Serena Williams comes back to defeat Yulia Putintseva 5-7, 6-4, 6-1 at the French Open.