But, true to form, Williams did not allow the temporary obstacle to shift her focus, and she forced Kvitova to hit wide on match point. Apparently, the time off has done her well. She won in London five times.
The question in this match against Anastasija Sevastova is whether Stephens has the patience and concentration to prepare herself for the longer rallies.
Here, too, were emotional storylines of triumph over adversity.
Despite being taken out, it the world No. 14 can take great heart from her displays in NY, which comes just nine months after being the victim of a knife attack in her home. "She can still win many titles". On Dec. 20, an intruder in her home in Prostejov, Czech Republic, about 125 miles southeast of Prague, attacked her with a knife and damaged the tendons in all five fingers on her left hand, with which she won two Wimbledons. En route to the last eight, she made no mistakes despite facing some risky opponents like Jelena Jankovic, Alize Cornet, Caroline Garcia or Garbine Muguruza.
But Williams dug deep, broke back thanks to a double fault and then held serve in a titanic ninth game.
But then the performance of Williams was proving pretty remarkable, too.
The 37-year-old's odds have tumbled through each round she has progressed, and before her quarter final match she was still available at 14/1 with one bookmaker. She played very well in the tie-break. "I was happy to have a little more luck today, actually".
This would be no different, in as compelling and intensely fought a contest as one could wish for. Four of them though are on the women's side.
Kvitova had saved five break points in the second set before she levelled the match, going to set point with a bold volley and converting it with a service victor. The Estonian reached her sixth Grand Slam quarterfinal with a dominating victory over Daria Kasatkina on Monday. After a quick break, she had to fight off break point, thumped a forehand, threw in a sliced drop shot, and completed the hold with a backhand victor, 3-0. But for Williams, when she was coming up in the game, it was situation normal. Williams has been struggling with serve-especially her second serve-which gives the edge to Kvitova. She is just more like every other tennis player in the draw - an independent, lone operator, trying to fulfill a personal dream. She had her hand in that splint for two months.
Although the match had been close throughout, the tie-break was mostly one-way traffic.
And once Williams got the bit between her teeth, she became an irresistible force.
Sevastova, who beat Maria Sharapova in the fourth round, used all manner of mixed speeds and angles against Stephens, often winning points with the help of drop shots.
Williams is the oldest woman entered at 37 but was this year's Wimbledon and Australian Open runner-up.
But four Americans in the semifinals? She lost to her younger sister Serena Williams at the Australian Open and to Garbine Muguruza at Wimbledon.
Asia has been fruitful ground for Kvitova in the past and she's hoping it will be again.