Naomi Osaka has continued her bid for a second straight US Open title with a business-like 6-3 6-4 win over Magda Linette to book her place in the third round.

After struggling with nerves in her gruelling first-round match, Osaka was calm and collected on Louis Armstrong Stadium court, smacking 13 winners and playing stout defence to dispatch Poland’s Linette on Thursday and set up a possible third-round showdown with Coco Gauff.

After a one-sided first set, trouble brewed for the world No.1 when Linette raced out to a 3-0 lead in the second on a sun-soaked court.

But the 21-year-old Japanese kept her composure and battled back, hitting a deft volley on match point to seal the win before an adoring crowd including former San Francisco 49er Colin Kaepernick and former Los Angeles Laker Kobe Bryant.

Next up for Osaka is either qualifier Timea Babos or 15-year-old American wildcard Gauff.

While Osaka moved on, another two-time grand slam champion was eliminated when sixth seed Petra Kvitova was upset by Andrea Petkovic 6-4 6-4.

Wimbledon champion Simona Halep will try to avoid falling when she played Thursday afternoon.

Meanwhile, Australian No.2 Ajla Tomljanovic fought hard in searing heat before bowing out 4-6 7-5 6-2 to Estonia’s world No.21 Anett Kontaveit.

Other early winners included No. 16 Johanna Konta, who routed Margarita Gasparyan 6-1 6-0; and No. 20 Sofia Kenin, who swept past Laura Siegemund 7-6 (7-4) 6-0.