Defending champion Naomi Osaka overcame a nervous start to scrape past Russian 20-year-old Anna Blinkova 6-4 6-7 (5-7) 6-2 in the US Open first round.
Wimbledon champion Simona Halep was also taken to a third set by American Nicole Gibbs but won 6-3 3-6 6-2.
And American 15-year-old Coco Gauff came from a set and a break down to beat Anastasia Potapova 3-6 6-2 6-4.
Osaka was 4-1 down in the opening set before she won five games in a row to take the lead.
In a second set riddled with errors, she saw off three sets points and held match point before losing a tie-break.
The world number one, who made 50 unforced errors in the match, fought off three more break points in the decider and will now face Polish world number 53 Magda Linette in round two.
Osaka avoided becoming only the seventh player to lose in the opening round of a women’s singles title defence at a Grand Slam, while defeat would have cost her the number one ranking.
Simona Halep took a fairly comfortable first set against Gibbs, ranked 135th, but despite holding off six set points, was broken for a fourth time late in the second.
But she cruised through the decider, breaking twice to ensure she avoided three successive first-round defeats in New York.
The fourth seed will face world number 116 Taylor Townsend, another American, in the second round.
Teenage sensation Gauff, who stunned Venus Williams on her way to reaching the fourth round at Wimbledon this year, faces Hungarian doubles specialist Timea Babos next.
Gauff, playing singles in front of a home crowd at Flushing Meadows for the first time, carried on the momentum she built this summer by producing another thrilling comeback.
She looked nervous in the opening set – hitting just three winners and 16 unforced errors – as the crowd were silenced by 18-year-old Potapova, who appeared to be in control when she broke again early in the second.
But Gauff, who saved two match points in an astonishing victory over Slovenian Polona Hercog in the third round at Wimbledon last month, broke back three times and went on to win the decider.
This latest victory comes in the same month she won her first WTA doubles title at the Washington Open alongside compatriot Catherine McNally, 17.
Two-time finalist Caroline Wozniacki overcame an early lapse against China’s Wang Yafan to set up a second-round match against Australian Open semi-finalist Danielle Collins.
A shock looked on the cards for the former number one when she went down 6-1 in the first set, but the Dane bounced back to take the next two sets 7-5 6-3.
There was, however, a first-round exit for two-time Grand Slam champion Garbine Muguruza, who lost 2-6 6-1 6-3 to Alison Riske.
American Riske, ranked 11 places below the Spaniard at 36th, sealed her first win at Flushing Meadows since 2013 and will take on former French Open champion Jelena Ostapenko in the second round.
Latvia’s Ostapenko overcame Serb Aleksandra Krunic 6-3 7-6 (7-9), while two-time Wimbledon champion and sixth seed Petra Kvitova beat fellow Czech Denisa Allertova 6-2 6-4.
Elsewhere, the 2017 champion Sloane Stephens was beaten 6-3 6-4 by qualifier Anna Kalinskaya, with the Russian claiming her first career Grand Slam win.
Former world number one Victoria Azarenka lost a Belarusian battle with Aryna Sabalenka.
Number nine seed Sabalenka came back from a set down to reach the second round in three sets 3-6 6-3 6-4.
Swiss 13th seed Belinda Bencic won 6-3 6-2 against Luxembourg’s Mandy Minella, while Dutch seventh seed Kiki Bertens defeated Spaniard Paula Badosa 6-4 6-2.
Croatia’s 23rd seed Donna Vekic overcame Richel Hogenkamp of the Netherlands 7-6 (7-4) 6-3.
And Canadian 15th seed Bianca Andreescu is through with a comfortable 6-2 6-4 win over American 17-year-old Katie Volynets.