Rafael Nadal
Nadal is through to the third round of the US Open Getty

Rafael Nadal overcame a slow start to defeat world number 121 Taro Daniel late on Thursday night (31 August) and book his place in the third round of the US Open.

With the shock exits of Grigor Dimitrov, Tomas Berdych, Alexander Zverev and Nick Kyrgios at Flushing Meadows so far, there was a possibility of yet another major departure when the American-born Japanese took the first set over Nadal.

However, the world number one soon got into his groove as he completely dominated Daniel from the second set onwards, eventually prevailing in a 4-6, 6-3, 6-2, 6-2 win.

"For me, it's a very important victory," Nadal said after the win. "It's true I didn't play very well tonight but at the same time it's true that I am through."

"I need to improve a lot of things but I am here to try to improve every day. I'm going to work tomorrow hard to find better feelings. I really believe I can do it much better."

The Spaniard will face world number 59 Leonardo Mayer next, who notably came through the qualifiers and upset 30th-ranked Richard Gasquet in the first round of the event.

Meanwhile, Roger Federer had to dig deep to overcome Russia's Mikhail Youzhny.

Taken all the way to the fifth set for the second time in three days, the Swiss ace fought back from being two sets down to eventually triumph over the 101st-ranked Youzhny in a 6-1, 6-7, 4-6, 6-4, 6-2 win in just over three hours.

Committing an uncharacteristic 68 unforced errors, with his subpar performance likely stemming from his pre-tournament back issues, Federer has now played in five-set matches in the first two rounds of a Grand Slam for the first time in his career.

"I think because you're on a high, you're thrilled that you got through, so you don't look at the negative," Federer said following his win. "Or I don't. Yes, I might feel more tired than I normally would going into a third round, but that's OK."

"My preparation hasn't been good at all here. I knew I was going to maybe struggle early on. Maybe I struggled more than I would have liked to. But I'm still in the draw, which gives me a chance."

"This match wasn't about the back, which is good. This is more just a grind. I felt different, completely different, the way it played and everything. But I'm really, really happy I got through."

Federer will now play Spain's Feliciano Lopez in the third round.