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.
“I don’t think I’ve ever been this nervous in my life,” Osaka told the crowd on Arthur Ashe court. “I came off really slow and never really found my rhythm. I fought as hard as I could and managed to win.
“You want to do well after you did well last year. I didn’t smile much playing this match so hopefully I can change that in the next match. It’s kind of just a game so I have to remember that.”
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.
The Japanese 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.
Romanian 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.
Gauff, who stunned Venus Williams on her way to reaching the fourth round at Wimbledon this year, faces Hungarian doubles specialist Timea Babos next.