Anastasija Sevastova US Open 2016
Anastasija Sevastova celebrates her upset victory over Garbine Mugurza in the second round of the US Open, Aug.31, 2016Reuters

The first big upsets of the US Open came on Wednesday when Garbine Muguruza, the No.3 seed and French Open champion, was bounced out by Anastasija Sevastova in the second round in New York, while Milos Raonic, the Wimbledon finalist, lost to Ryan Harrison.

Muguruza, who has not had the best of times on the hard courts, was knocked out of the final Grand Slam of the year 7-5, 6-4 in one hour and 39 minutes by the world number 48.

Raonic looked good for the third round after winning the first set against Harrison, but the American held his nerve in the next three, eventually coming up trumps 6-7 (4-7), 7-5, 7-5, 6-1.

Novak Djokovic got the much-needed rest he was looking for, after Jiri Vesely, who had come through a difficult five-setter against India's Saketh Myneni in the first round, gave the Serbian a walkover.

Djokovic was not exactly convincing in his first round match at the US Open 2016, against Jerzy Janowicz, struggling to find his usual rhythm, while also receiving treatment for an arm problem.

So, to get a bit more rest for a wrist injury, which he has struggled with coming into this US Open, and give more time for the arm problem to heal will be welcomed, especially considering the humid conditions at play in New York on Wednesday.

Rafael Nadal is another one who came in with a few injury doubts, but after easing into the second round on opening day, the Spaniard put in another impressive performance, topping Andreas Seppi in straight sets 6-0, 7-5, 6-1 in the final match of the day at the Arthur Ashe Stadium.

Crowd favourite Gael Monfils also had a comfortable outing, beating Jan Satral of the Czech Republic 7-5, 6-4, 6-3. It wasn't quite as straightforward, though, for his French compatriot Jo-Wilfried Tsonga, who had to overcome a second set blip to get the better of Australian James Duckworth 6-4, 3-6, 6-3, 6-4.

"It was a good match," Tsonga said. "I played well. I don't know what he (Duckworth) will say, but I think it was a good level. I saw the statistic after the match, and, yeah, I served well. I returned well.

"The only thing, I had – I did only four breaks on my 25 break points. That is the only dark things on my statistics. (But), I'm pretty happy the way I played."

John Isner and Jack Sock kept the American hopes alive with victories over Steve Darcis and Mischa Zverev respectively, while title contender Marin Cilic moved into the third round. Cilic eased past Sergiy Stakhovsky 6-1, 6-2, 6-3.

In the women's singles, Caroline Woznicaki showed signs of the kind of form that took her to the world number one ranking a few years back, outclassing the experienced Svetlana Kuznetsova, seeded nine, 6-4, 6-4. Petra Kvitova also moved into the third round of the US Open after seeing off the challenge of Cagla Bayukakcay 7-6 (7-2), 6-3.

The US Open 2015 finalist Roberta Vinci is also in the third round, after the Italian's 6-1, 6-3 win over American Christina McHale. The No.2 seed Angelique Kerber stayed on course to take the No.1 ranking away from Serena Williams with a 6-2, 7-6 (9-7) victory over Croatian Mirjana Lucic-Baroni.