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Sloane Stephens began the defence of her US Open title with a 6-1 7-5 victory over Russia's Evgeniya Rodina.
The American, whose 2017 win earned her a first Grand Slam, broke twice on her way to taking the first set.
Stephens broke again in the first game of the second set and at 5-4 was heading towards victory before her own serve was broken for the first time.
But the number three seed broke back to love in the next game before holding serve to book her spot in round two.
She will now face 21-year-old Ukrainian Anhelina Kalinina, who is competing in the main draw of a Grand Slam for the first time and defeated Liechtenstein's Kathinka von Deichmann on day one.
American two-time champion Venus Williams also progressed to round two, to the delight of the home crowd. The 38-year-old, a winner in 2000 and 2001, defeated 2004 winner Svetlana Kuznetsova of Russia 6-3 5-7 6-3 in just under three hours.
Williams will now play Italy's Camila Giorgi, who reached the quarter-finals at this year's Wimbledon.
Poland's Agnieszka Radwanska went into the tournament with a record of never having lost a first round match in 12 previous visits. However, that record ended with a 6-3 6-3 defeat to Germany's Tatjana Maria.
Seventh seed Elina Svitolina of Ukraine overcame the USA's Sachia Vickery 6-3 1-6 6-1 to reach the next round, as did Czech number eight seed Karolina Pliskova, who defeated Kazakh Zarina Diyas 6-4 7-6 (7-4).
Spain's Garbine Muguruza, winner of the 2016 French Open and 2017 Wimbledon titles, beat China's Zhang Shuai 6-3 6-0.
And two-time finalist Victoria Azarenka of Belarus defeated Slovakia's Viktoria Kuzmova 6-3 7-5 to secure a spot in the second round.
