Images from the US Open men's singles first round matches, at Flushing Meadows, New York, on Tuesday.
Nadal, who got a first-round bye, defeated Richard Gasquet 6-3, 6-4 to advance.
Heading into the final, Gauff had lost the first set in three straight matches and the former U.S. Open champion seemed determined to buck that trend, serving to love in the opening game and breaking early for a 2-0 lead.
Spanish fourth seed Garbine Muguruza fine-tuned her preparations for this month's U.S. Open by crushing Simona Halep 6-1, 6-0 in the Cincinnati Open final on Sunday.
Victoria Azarenka won a showdown between the world's two top players by beating number one Serena Williams in a three set 2-6, 6-2, 7-6 thriller in the final of the Western and Southern Open on Sunday.
Top seed Ash Barty rallied from a set down to power into the semi-finals of the Cincinnati Masters on Friday.
Alcaraz, winner of the last two Grand Slams at Roland Garros and Wimbledon, had made it to at least the quarter-final stage at every major in which he has competed since winning the US Open two years ago.
The top seeds scored a straight sets victory over the Colombian-Chinese pair of Catalina Castano and Meng Yuan.
World number one Serena Williams was at her lethal best as she crushed Romanian Simona Halep 6-0, 6-4 to romp into the semi-finals of the Western and Southern Open on Friday.
They were beaten by the top-seeded pair of Maria Elena Camerin and Gisela Dulko.
Naomi Osaka has four major titles under her belt but the second round at Flushing Meadows, Wimbledon and Roland Garros was as good as it got this year for the Japanese 26-year-old, who exited the Australian Open in the first round.
Tiger-tattooed Aryna Sabalenka clawed her way back from injury and disappointment to hoist the US Open trophy at last.
Serena Williams' scored a ruthless 6-3, 6-1 win over Bethanie Mattek to advance to the quarter-finals of the Cincinnati Open
Serena Williams finished her last U.S. Open tune-up in style by blowing away Serbian Ana Ivanovic 6-4, 6-1 to win her first title at the Western and Southern Open in Cincinnati on Sunday.
Russia's Maria Sharapova will face Serbia's Jelena Jankovic in the Cincinnati Open final after the pair enjoyed solid victories in their semi-finals on Saturday. Sharapova recovered from a poor start to beat fellow-Russian and world number two Vera Zvonareva 2-6, 6-3, 6-3 to reach her fourth final of the season while Jankovic beat Germany's Andrea Petkovic 7-6, 6-1.
World number two Rafa Nadal scraped into the quarter-finals of the Cincinnati Open after beating fellow Spaniard Fernando Verdasco 7-6, 6-7, 7-6 in a fierce battle on Thursday but his rivals all had comfortable paths into the last eight.
The seventh-seeded Bulgarian advanced to his eighth ATP World Tour Masters 1000 quarter-final with a 6-3, 7-5 victory over Del Potro, who struggled with the intense heat in the closing stages of the one hour, 39 minute match.
Olympic and Wimbledon champion Andy Murray picked up where he left off in Rio by drubbing Argentina's Juan Monaco to take his place in the third round of the Western & Southern Open in Cincinnati on Wednesday.
Madison Keys beat fellow American CoCo Vandeweghe for the second time in eight days with a 6-4, 3-6, 6-3 victory on Monday to reach the second round of the Cincinnati Open.
Top-seed Jelena Jankovic and second seed Caroline Wozniacki suffered surprise third-round exits in the Cincinnati Open on Thursday.
The Indian ace beat Anna-Lena Groenefeld 6-4, 6-3 in the first round of the Western and Southern Financial Group Women's Open
Reader Abhishek Sikri sent us a picture of Rohan Bopanna from the USA.
Carlos Alcaraz said he will be "at 100%" for the US Open despite stopping his training in New York on Saturday as a precaution after twisting his ankle.
Rafa Nadal urged tournament organisers to make more consistent surfaces for hard court events after easing past American Taylor Dent 6-2, 7-5 to make the third round of the Cincinnati Masters on Wednesday.
Mahesh Bhupathi and Max Mirnyi advanced to the men's doubles quarter-finals of the Cincinnati Masters after getting a walk over. Fourth seeds Bhupathi and Mirnyi were scheduled to play against Americans John Isner and Sam Querry, who withdrew from the contest due an ankle injury to Isner.
Nick Kyrgios has been fined $113,000 by the ATP for arguing with the chair umpire and smashing two rackets during his second-round loss at the Cincinnati Masters.
Rafael Nadal continued his perfect run on the North American hardcourts taming Czech Tomas Berdych 7-5, 7-6 (4) at the Western and Southern Open on Saturday to setup a final showdown with big-hitting American John Isner.
World number one Dinara Safina will take on a rejuvenated Jelena Jankovic in the final of the Cincinnati Open after hugely contrasting wins on Saturday. Russian Safina stormed into her eighth final of the year with a 6-2, 6-0 demolition of Italian Flavia Pennetta, while fifth seed Jankovic saved four match points to beat fourth seed Elena Dementieva 7-6, 0-6, 7-6 after two hours and 46 minutes.
Novak Djokovic is returning to the US for the first time in two years after being denied entry due to being unvaccinated for COVID-19.
Serena Williams, coming off a double Olympic gold medal-winning performance in London, said she was feeling the pace of a hectic schedule after a lethargic display in her 6-3, 6-0 win over Urszula Radwanska on Thursday.
World number one Dinara Safina scrambled past Italian Roberta Vinci 2-6, 7-5, 6-4 to reach the third round of the Cincinnati Open on Tuesday. World number 46 Vinci served for the match at 5-4 in the second set but her nerve failed her at the crucial time.
Novak Djokovic begins his hunt for a fifth Flushing Meadows crown when he meets Moldovan Radu Albot
The Indo-Czech duo advanced after fifth seeds Paul Hanley and Kevin Ullyet withdrew while trailing 3-5 in the first set.
The Cincinnati Open claimed two more high-profile victims on Thursday with Grand Slam champions Li Na and Petra Kvitova crashing out, while Russian pair Maria Sharapova and Vera Zvonareva crunched their opponents en route to the quarter-finals.
While her career has featured a number of highs -- she has won two doubles Grand Slam titles and 11 WTA titles, including the Cincinnati Masters -- Garcia said she has become fixated on what she sees as her failures.
Mahesh Bhupathi and Jamie Murray fell to top seeds Mike and Bob Bryan in the second round.
Making her first semi-final appearance after quarter-final exits at each of the last two editions of the tournament, Sania confessed that she ran out of steam towards the end.
Rafael Nadal and Roger Federer, numbers two and three in the world, suffered surprise defeats to Mardy Fish and Tomas Berdych respectively in an entertaining quarter-finals day at the Cincinnati Open on Friday.
