American Sloane Stephens edged past 16th seeded Latvian Anastasija Sevastova 6-3 3-6 7-6 (4) to book her place in the semi-finals.
Reaching the last eight in the final Grand Slam of the season was an impressive achievement for Kvitová, who was playing only her eighth tournament since requiring major surgery on her left hand after an attack at her home last December.
A U.S. Open title is just three wins away, and Serena Williams is busy with her newborn daughter, leaving her throne unguarded. "So it's great to see this resurgence, and I hope it can continue".
"I don't think that I can find the right words". But at 37 and with seven Grand Slam titles to her name, those are footnotes to major wins, and it's tough to get motivated for footnotes.
"It's been a really great ride in the last week", Sharapova said afterward. And, it was there that Williams heeded her own advice, from her on-court interview after her fourth round win on Sunday, "Nobody ever gives you a Slam". "I was anxious about my protected ranking and not having enough tournaments and not being able to play and there were just so many things I was anxious about".
It's the first all-American US Open women's semifinal since Serena Williams defeated Lindsay Davenport in 2002.
After an early exchange of second-set breaks, Carreno Busta broke to 5-4 and held to claim the set, then broke at love on a double fault to open the third set. Each of their previous five meetings - four of which had been won by Kvitova - had also gone to a third set. "It was something really special for me".
Despite the familiarity of the surroundings and the overwhelming amount of good wishes from fellow players and supporters, her return to the tennis spotlight has been a huge challenge over many weeks and months. "Just happy to be playing really well and happy that my foot is good and I don't have any pain and my body is holding up", she said.
"It came down to the wire and I'm hoping we have more matches like that".
Kvitova ensured there was no repeat of her first-set collapse, fending off five break points to level the match and force a decider. Kvitova took three of her four break points in the match while Williams converted just three of her 11.
With the Ashe crowd behind her in the final set tiebreak, Williams willed her way to a 5-1 lead and when Kvitova sailed a return wide for 6-2, the American sealed the victory. And it has endured, through illness and distractions, an ambitious father, and a younger sister who raced ahead of her and emerged as the greatest player of all time.
Asked about some of the remarkable comeback stories which this tournament has produced, Williams said: "I think sport is a little microcosm of life". Like she would hit these incredible shots out of nowhere, and all I could do was say, "well done". "Before, I was playing well, I had won a couple tournaments and was playing well". Even more so when she had a point for a 4-2 lead.