Defending champion Sloane Stephens fought back from a set down to beat world number 134 Anhelina Kalinina and progress to the US Open third round.
The American third seed, treated for blisters in the second set, won 4-6 7-5 6-2 in two hours and 46 minutes.
Sloane Stephens returns a shot with a powerful double backhand
She faces Belarus' Victoria Azarenka next, after the former world number one beat Daria Gavrilova 6-1 6-2.
Ukrainian seventh seed Elina Svitolina also progressed with a 6-2 6-3 win over Germany's Tatjana Maria.
The 21-year-old will play the winner of the match between Qiang Wang and Irina-Camelia Begu in the third round.
Having lost an enduring opener in an hour and two minutes, Stephens broke three times in the second set only to be pegged back to 5-5 by Kalinina after receiving treatment for blisters on her hand.
The 25-year-old eventually closed out the set and, despite going a break down in the first game of the decider, proved too strong for the 21-year-old Ukrainian, who was playing in the main draw of a Grand Slam for the first time.
Stephens, who said she had "two bites of sushi and a slushy" during the 10-minute heat break before the final set, bemoaned the conditions on Arthur Ashe Stadium.
"It was super hot," she added. "I was sweating a lot and it was not ideal conditions, but I am happy to get through.
"I hope that I play a little bit better than today [in the next round], go out and compete hard."
Maria Sharapova survived Patty Schnyder scare to advance into the second round
Sharapova in second round
Meanwhile, five-time Grand Slam champion Maria Sharapova held off a spirited fightback from Swiss veteran Patty Schnyder to reach the second round of the US Open.
The Russian defeated Schnyder - who, at 39, is the oldest player ever to make the main draw of a Grand Slam via qualifying - 6-2 7-6 (8-6).
The match was Schnyder's first in a Grand Slam since she came back to tennis in 2015 having retired in 2011.
"I knew I was in for a battle no matter her story or my story," said Sharapova.
"For her to come back and have the desire is really admirable. I'm just really happy I was able to win that last point."