Serena Williams a while ago shrugged off slow start to emerge victorious over fellow American 17-year-old prodigy Caty McNally 5-7 6-3 6-1.
Earlier, Roger Federer came from a set down to beat Damir Dzumhur 3-6 6-2 6-3 6-4 under the Arthur Ashe Stadium roof to reach the US Open third round.
The world number three hit 17 unforced errors in losing the first set.
But the Swiss five-time champion dominated the remainder of the match to defeat Bosnian world number 99 Dzumhur.
Victory for the 38-year-old sets up a third-round match against either Britain’s Dan Evans or Frenchman Lucas Pouille at Flushing Meadows.
Federer dropped the opening set in his first-round win over Indian qualifier Sumit Nagal and he made another slow start here, losing the first four games of the match.
“I don’t think there is a secret to a good start other than warming up well, being well prepared mentally and not underestimating your opponent. I did all of that,” said Federer, after a match played under the roof because of rain in New York on Wednesday.
“So when it happens in back-to-back matches it’s a bit frustrating more than anything, especially when the level is that low and there are that many errors and the energy is not kind of there.
“But I’m not concerned because once I lose that first set I do get better, which is a good thing.”
After serving out the first set, 27-year-old Dzumhur held a break point in the opening game of the second set but could not convert.
Federer then immediately broke with a forehand winner and levelled the match through another break when Dzumhur double-faulted.
The Swiss broke at the first opportunity in the second set but had to save four break points in the seventh game as Dzumhur continued to push him.
After sealing the set with an ace, a forehand winner allowed Federer to break in the third game of the fourth set and he went on to seal victory in two hours and 22 minutes.
Federer hit 16 aces to Dzumhur’s two and 58 winners overall – more than double his opponent’s 26.
Similarly, Fifth seed Elina Svitolina had five match points saved before she eventually defeated Venus Williams 6-4 6-4 to reach the US Open third round.
The Ukrainian, 24, missed several opportunities to seal the win in a 17-minute ninth game of the second set.
She eventually secured victory when a forehand from 2000 and 2001 champion Williams, 39, went long.
Earlier, third seed Karolina Pliskova reached the third round with a straight-set win over Mariam Bolkvadze.
Wimbledon semi-finalist Svitolina, who has reached the fourth round at Flushing Meadows in the past two years, will now play either Rebecca Peterson of Sweden or compatriot and 32nd seed Dayana Yastremska.
“It was an incredible match. We saw it was incredibly tough and only a few points divided the match,” said Svitolina.
Pliskova, 27, dominated to win 6-1 6-4 against Georgian Bolkvadze, ranked 202 in the world, under the roof on Arthur Ashe Stadium.
The Czech, a finalist in 2016 at Flushing Meadows, hit nine aces in 66 minutes to maintain her bid to regain the world number one ranking.
She faces either Tunisian Ons Jabeur or Belarusian Aliaksandra Sasnovich next.
Meanwhile, 24-year-old Madison Keys became the first American to advance to the third round with a 6-4 6-1 win over China’s Zhu Lin.
She will face either Sofia Kenin or Laura Siegemund in the next round.
Britons Johanna Konta and Dan Evans will play their US Open second-round matches on Thursday after Wednesday’s matches on the uncovered outside courts were cancelled because of rain.