Stephens had a tough outing and was pushed to three sets in her last match against Julia Görges, the 30th seed, but she prevailed and will now try and down Sevastova, who herself had a tough match against Maria Sharapova, but prevailed in three sets.
Steen: A wonderful matchup between in-form players who are peaking at the right time.
You're up, Coco Vandeweghe and Madison Keys. "I can not imagine playing at 37, but she likes it and she has the motivation".
Stephens made her comeback from a foot injury only at Wimbledon and was ranked world No 957 at the end of July.
Sevastova thought she had a harder time dealing with the jitters presented by the occasion than Stephens did, even acknowledging that she relied less on drop shots late because those require gumption she couldn't quite muster.
Here, too, were emotional storylines of triumph over adversity. "All I have known all my life was great American players, so it's great to see this resurgence. She can still win many titles". No matter: the power game and steely determination of the Czech saw her producing her best tennis since her return. 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 then the performance of Williams was proving pretty remarkable, too. Her victories were in 2000 and 2001 so the 37-year-old is eager to add another to the tally.
But can she fight off American powerhouse CoCo Vandeweghe, a player that is firing all cylinders in NY? She also said, "I'm not sure if it is the result of what happened, but maybe I feel a bit fearless, I think, because of what happened".
When Kvitova moved ahead and emphatically saved three break points from 0/40 down in the fourth game, victory seemed hers for the taking. With both women hitting huge ground strokes and crunching serves as they attempted to dictate the rallies at the first opportunity, most of the exchanges were short. She has reached the semis only twice since then. As always, Williams remained unperturbed by her own errors or the strong play of her opponent, and eventually overcame a 1-3 deficit in the first set by winning the next five games to take the set 6-3. For a moment, it looked like the match might take another turn, as Williams double faulted on her first match point. She's refreshed, engaged and playing some of the best tennis of her career. She had her hand in that splint for two months. Kvitova did not waver, serving to love, and yet again, their contest would be decided by a tie-breaker.
"Life is still a little bit odd, but it's getting better as well", she admitted this week.
She will face Sloane Stephens in the semifinal after Stephens outlasted Anastasija Sevastova in a third-set tiebreak during Tuesday's early action.
Williams has reached the finals at the Australian Open and Wimbledon this year, and is in contention to win a thirdUS Open 20 years after making the final on her debut.