Remarkably, however, Konta -- who could be heard saying her heart rate increased and suggested her vision was blurred after she had dropped to the court -- recovered to join Wozniacki in the third round in New York.
Wozniacki -- whose season has been blighted by ankle and arm injuries -- achieved her best grand slam showing of 2016 by winning a round and the former No. 1 went one better Wednesday by defeating 2004 U.S. Open champion Svetlana Kuznetsova 6-4 6-4.
Wozniacki, now ranked 74th, lost to Kuznetsova in the first round at Wimbledon but improved to 3-0 against the world No. 10 at the U.S. Open after a shaky start: Kuznetsova led 4-0 in the opening set.
Indeed Wozniacki wasn't about to throw in the towel in the city she loves and owns an apartment in.
The U.S. Open has also been Wozniacki's most successful major.
Two years ago, after a much publicized split from golfer Rory McIlroy that left her reeling, Wozniacki signaled a return to form by making a second U.S. Open final. Months later, she completed the New York marathon.
She isn't discounting another long stay at Flushing Meadows.
"At the end of the day, I know my worth," Wozniacki told reporters. "I know how good I can play. I know that with hard work hopefully I can get back there.
"Today was definitely a step in the right direction. I'm really proud of the way I just kept fighting. You know, I'm just enjoying myself and happy that I get another chance in two days."
En route to the final in 2014, Wozniacki's opponent in the semifinals, Peng Shuai, suffered from a heat-related illness. Cramping, Peng retired from the match and left the court in a wheelchair.
The scenes were similar as Konta faced Tsvetana Pironkova on Court 13. Serving at 5-6 in the second set, the conditions -- temperatures hovered around 30 degrees Celsius with high humidity -- took their toll on the world No. 14.
Konta slowly dropped to the court before being given ice packs by the chair umpire, Julie Kjendlie. A significant delay ensued -- while the trainer and a tournament doctor got to the court -- before Konta, who had her blood pressure checked, slowly walked to her chair.
This year's Australian Open semifinalist decided to play on and upon the resumption, hit her second serve long to give Pironkova the set.
Konta then took a lengthy toilet break between sets and by the time she returned, one point had been played in roughly 25 minutes.
Now with more energy and with Pironkova -- a former Wimbledon semifinalist -- bewildered, Konta prevailed 6-2 5-7 6-2.
Konta will hope to be ready to play Friday when she is scheduled to encounter Belinda Bencic, the young Swiss whose ranking tumbled recently because of back and wrist injuries.
One player who won't be around is Garbine Muguruza. Muguruza won the French Open in June to open her grand slam account but has since struggled with illness -- and expectations. She was defeated by Latvia's Anastasija Sevastova -- who retired from tennis in 2013, only to return -- 7-5 6-4.
In another upset, Wimbledon finalist Milos Raonic lost to U.S. qualifier Ryan Harrison 6-7 (4-7) 7-5 7-5 6-1. Raonic, like Konta, struggled with cramps.
"I don't think hydration was an issue," said the Canadian. "I think I always take that precaution. Probably just nerves and stress, a mental sort of overexuberance."
No struggling for Djokovic
Men's No. 1 Novak Djokovic, perhaps, needed a break after dealing with a left wrist and right arm injury in a first-round victory. He got one Wednesday, advancing without taking to the court when opponent Jiri Vesely withdrew due to a forearm complaint. Vesely upset Djokovic in Monte Carlo in April.
Djokovic next meets Mikhail Youzhny, a one-time U.S. Open semifinalist, after the Russian veteran dispatched Guido Pella 6-2 6-1 7-6 (7-3).
Djokovic is bidding to win a 13th major, which would put the Serb one behind both Pete Sampras and Rafael Nadal and a mere four behind men's leader Roger Federer.
Nadal -- who is playing with a wrist injury himself -- went through comfortably, downing Andreas Seppi 6-0 7-5 6-1. History was made in the night match on center court when the newly installed roof was used for the first time in tournament history when rain began to fall.