NEW YORK -- They were just two particular points from Serena Williams' latest three-set comeback at the US Open, yet they were pivotal and consisted of the sorts of lengthy exchanges filled with athleticism and brilliance that in any other, non-pandemic year would be marked by thousands of folks rising to their feet for delirious roars and raucous applause.
She needed both of these points, one of which included a shot she hit left-handed, to reverse a deficit that reached the scale of a set and a break after 45 minutes of her quarterfinal against Tsvetana Pironkova on a cloudy Wednesday in empty Arthur Ashe Stadium.
Williams needed both of these points during a five-game, match-altering run -- along with 20 aces, her most in a match in eight years -- to end up on the right side of a 4-6, 6-3, 6-2 score after more than two hours to get to the semifinals at Flushing Meadows for an 11th consecutive appearance.
"It's not how you start, it's how you finish, right?" Williams said.
Two more victories would allow her to claim a record-tying 24th Grand Slam singles title.
"In the beginning, I was a little fatigued, for whatever reason," Williams said. "Obviously, I can't do that if I want to keep winning, so I need to figure that out."
How big an upset would this have been if Pironkova had held on? Not only is she not seeded at Flushing Meadows, she doesn't even appear in the WTA rankings at all -- this was her first tournament of any sort in more than three years, because she left the tour to become a mother.
"It's unbelievable," Williams said about Pironkova's impressive return to competition. "Wow. I couldn't even do that."
When the players stepped out onto the court, the stadium announcer -- announcing for whom, exactly, was something of a mystery -- referred to Pironkova, a 32-year-old from Bulgaria, as "Alexander's mom" and then to Williams as "Olympia's mom" during the pre-match introductions.
"It just shows me how tough moms are," Williams said afterward.
"You play a match and you go home and you're still changing diapers," said Williams, whose daughter turned 3 on Sept. 1 and is a little older than Pironkova's son. "It's like a double life. It's really surreal."
The American, who turns 39 in less than three weeks, has won six US Open championships; she was the runner-up the past two years.
Williams last lost before the semifinals in New York in 2007, when Justine Henin eliminated her in the quarterfinals.
On Thursday, Williams will face Victoria Azarenka, who returned to the US Open semifinals for the first time since 2013 by overwhelming Elise Mertens 6-1, 6-0 on Wednesday night.
Williams leads her head-to-head series against Azarenka 18-4, including beating her in the 2012 and 2013 finals in New York. It was in a 2012 match against Azarenka at Wimbledon that Williams last topped 20 aces, producing 24.
The other women's semifinal Thursday will be 2018 champion Naomi Osaka vs. No. 28 seed Jennifer Brady.
Williams also needed a comeback and the maximum number of sets to get through the fourth round before defeating 15th-seeded Maria Sakkari 6-3, 6-7 (6), 6-3.
In Wednesday's turnaround, the first key moment involved 24 strokes, the next-to-last a cross-court forehand by Williams from wide of the doubles alley, and the last an on-the-run squash forehand by Pironkova that landed in the net. That gave Williams a break and a 5-3 edge in the second set.
Williams raised her left fist as her husband yelled from his front-row corner seat; Pironkova put a hand on her knee, smiled ruefully and squatted behind the baseline.
The other came in a four-deuce opening game of the final set, and began with the right-handed Williams taking a page out of old friend Maria Sharapova's playbook by hitting a left-handed return of serve. Another 15 strokes followed, with Williams smacking a forehand passing shot that Pironkova volleyed into the net tape.
"That was intense," Williams said. "I was just trying to do everything I can -- whether righty or lefty."
Pironkova dropped onto her back, chest heaving; she left so much sweat on the court that a ball person was beckoned to wipe it away with a towel. That afforded Williams a third break point, which was converted for a 1-0 lead when Pironkova sent a forehand long.
"She definitely played like the champion she is," Pironkova said.
Williams then only added to the lead, her strokes finding targets better the longer the match went on. Her serve was especially good, as it usually is.
In contrast, Pironkova began to have more trouble on the longer points that she dominated early; she won the first half-dozen that lasted 10 strokes or more before Williams found more success.
A couple of times, Pironkova drew Williams forward with a drop shot, then took the point with a perfectly arced lob.
"I tried everything," Pironkova said.
But after compiling only five unforced errors in the first set, Pironkova had 21 over the last two.
Williams, in contrast, made 11 in the first set, just 13 the rest of the way.
"Definitely, the first set, I think I was in control of the match. I was doing all kinds of shots, and everything went ... my way," Pironkova said. "But, you know, I was expecting (that) it's not going to last forever."
The Associated Press contributed to this report.