Serbia's Novak Djokovic climbed one spot up to the second, after claiming the Shanghai Masters title for the fourth time in a row on Sunday.
Roger Federer reached the semi-finals on Friday by beating eighth-seeded Kei Nishikori 6-4, 7-6 (4). His first two matches both went three sets.
Federer, the defending champion, beat Daniil Medvedev 6-4, 4-6, 6-4 in the second round despite being broken late in the second set.
Roger Federer earlier put Team Europe ahead by saving three match points for a 6-7, 7-6, (10-7) victory over John Isner.
Federer and Djokovic took the first set 7-6 in a tiebreaker, but Sock and Anderson won the second set 6-3 and then captured the deciding tiebreaker 10-6.
Djokovic moved a step closer to a third championship at Flushing Meadows and 14th Grand Slam title overall by eliminating John Millman, who conquered Roger Federer in quarterfinals of US Open 2018.
Roger Federer suffered a shocking 3-6, 7-5, 7-6 (7), 7-6 (3) defeat to 55th-ranked John Millman of Australia in the fourth round of the 2018 US Open.
The No. 2-seeded Federer moved into the fourth round at Flushing Meadows for the 17th consecutive appearance. He's won five titles at the U.S Open, although the last arrived a decade ago.
Federer was crisp in a 7-5, 6-4, 6-4 win over Benoit Paire in and made it 18 of 18 lifetime in the second round of the U.S. Open.
For years, actually, Federer has dealt with questions about when he might retire. In part, that's because elite tennis players often used to become not-so-elite by the time they passed the age of 30.
Federer saved the first eight break points he faced before finally faltering by pushing a forehand long on the ninth.
The Swiss maestro had won five titles in a row in Flushing Meadows and was a game away from a sixth in 2009 when Juan Martin del Potro pulled out a fourth-set tiebreaker, then won the fifth set.
A six-player team from Europe will face a team of players from the rest of the world in the second year of the competition on Sept. 21-23.
Djokovic finally mastered the one tournament that's eluded him, beating nemesis Roger Federer 6-4, 6-4 on Sunday.
Federer and Williams were making their first appearance at the tournament since they each won the title in 2015. Williams opened with a straight-set victory against Daria Gavrilova.
Federer seeded second, has won in Cincinnati a record seven times but hasn't played there since winning in 2015. In 2016 he had a knee injury, and in 2017 he had back problems.
Nadal will now look to bounce back in the Rogers Cup, a build-up to the US Open where he will be defending his title.
Nadal said it was "an exceptional circumstance" that he has remained on top of the tennis world after turning 30, alongside Federer, 36, and Djokovic, 31.
That trio has combined to win 10 of the past 14 championships at Flushing Meadows: Five for Federer, three for Nadal, two for Djokovic.
Federer had a match point at 5-4 in the third set, but struck a backhand into the net before the eighth-seeded Anderson broke in the following game and held serve.
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