Serena Williams made to battle against Bertens

The world number one trailed 4-0 in the opening tie-break but came back to win 7-6 (7-5) 6-3 at Arthur Ashe Stadium.

Top men's seed Novak Djokovic had little trouble overcoming Andreas Haider-Maurer 6-4 6-1 6-2.

Buteighth seed Rafael Nadal was tested during his 7-6 (7-5) 6-3 7-5 victory over Diego Sebastian Schwartzman

The Spaniard, who trailed 5-3 in the first-set tie-break and fell a break behind in both the second and third sets, admitted he had to fight for the victory.

Elsewhere, defending champion Marin Cilic returned to the Arthur Ashe stadium for the first time since winning the title last year with a 6-2 6-3 7-5 win over Evgeny Donskoy.

Grigor Dimitrov made another early Grand Slam exit as the 17th seed, a Wimbledon semi-finalist in 2014, was beaten 6-3 7-6 (7-2) 2-6 4-6 6-4 by Mikhail Kukushkin, the world number 56.

Tenth seed Milos Raonic overcame a back problem to beat Fernando Verdasco 6-2 6-4 6-7 (5-7) 7-6 (7-1), women's 25th seed Eugenie Bouchard beat Polona Hercog 6-3 6-7 (2-7) 6-3, while Venus Williams saw off Irina Falconi 6-3 6-7 (2-7) 6-2.

Two down, five to go

The scream after the first set and the grimace at the end of the match were evidence that Williams was far from her best, but the 33-year-old is now five wins from her 22nd major title and the first calendar Slam in 27 years.

Bertens, ranked 110th, took an early lead and served for the first set but could not convert, and the Dutch qualifier then let a 4-0 lead slip in the tie-break.

Williams has spent much of her Grand Slam year fighting back from slow starts, however, and said afterwards: "It definitely doesn't worry me. I think being down a lot, I know I can try to make a comeback."

The six-time US Open champion would end the match with 10 double faults, and 34 errors to 23 winners, and was just happy to get the job done in straight sets.

"I've been really relaxed, but today I was a little tight and and I think it showed," she said.

(BBC)