US Open, Flushing Meadows
Dates: 30 August - 12 September Start time: 1600 BST
Coverage: Live text commentary on BBC Sport website and mobiles; updates on BBC Radio 5 live; live on Sky Sports
Nadal, who reached the semi-finals in 2008 and 2009, has yet to drop a set
Rafael Nadal cruised past Gilles Simon with an emphatic 6-4 6-4 6-2 win to book his US Open fourth-round spot.
The top seed, yet to reach a final at Flushing Meadows, edged the first set before serving out to win in two hours.
The Spaniard, 24, will next play 23rd seed compatriot Feliciano Lopez who progressed after Sergiy Stakhovsky was forced to retire with a toe infection.
Sam Querrey shocked 14th seed Nicolas Almagro, while eighth seed Fernando Verdasco defeated David Nalbandian.
Day seven saw six Spaniards progress into the fourth round, but one of those who did not have such a great day was Almagro, overcome in straight sets by the American 20th seed Querrey.
The 22-year-old Querrey, the youngest player left in the tournament, served magnificently throughout to win 6-3 6-4 6-4 and set up a fourth-round clash with Switzerland's Stanislas Wawrinka.
Nadal, looking for his first US Open crown, was up against a Frenchman slowly returning to full fitness after a year of problems with a knee injury.
A break in the third was enough to bag the first set for this year's French Open and Wimbledon champion and despite a tighter second-set battle, the eight-time Grand Slam winner was within a set of victory after a break in the seventh game.
The 42nd-ranked Simon, who became a father on Thursday, appeared to tire quickly after a torrent of ferocious forehands as Nadal swiftly wrapped up another straight-sets win.
"It was important to win without dropping a set," Nadal said. "Every day I seem to play much better which is good for my confidence."
The world number one will next play Lopez after Stakhovsky of Ukraine was forced to withdraw while trailing 6-3 4-0.
David Ferrer, seeded 10, was another victor after easing past his fellow-Spaniard Daniel Gimeno-Traver 7-6 (7-2) 6-2 6-2.
Verdasco had looked short of form in Toronto and Cincinnati
The 28-year-old rarely showed the form that took him to the semi-finals in 2007, beating Nadal on the way, but it was enough to see him progress after coming through an opening set tie-break.
For a place in the quarter-finals, Ferrer will face Verdasco, another Spaniard who secured his fourth-round spot with a 6-2 3-6 6-3 6-2 win over Argentina's injury-prone Nalbandian.
The eighth seed settled quickly to easily take the first set, before the 2005 US Open quarter-finalist recovered to take the next set.
But back came Verdasco, a quarter-finalist at Flushing Meadows last year, and despite looking in trouble at 2-3 in the third he stormed to four games in a row en route to a fine victory in 166 minutes.
Verdasco got through round three at a Grand Slam for the third time this year and faced only one break point on his serve in the three sets he won.
After defeating the Argentine, who was playing in his first Grand Slam since the 2009 Australian Open because of a series of injuries, Verdasco said: "I think mentally I was really strong, even in the first set.
"I was there all the time. You know, I felt positive and really good and focused."
Tommy Robredo was the final Spaniard into the last 16 as Frenchman Michael Llodra retired from their match with Robredo leading 3-6 7-6 (8-6) 6-4 2-1.
The 28-year-old will be looking to make the quarter-finals for the first time after falling at the last-16 stage six times so far in his career.
Mikhail Youzhny will stand in his way after the 12th seed beat John Isner 6-4 6-7 (7-9) 7-6 (7-5) 6-4.
Youzhny looked set to make swift progress as he went a double-break up in the second set after claiming the only break of the opener.
But to the delight of the crowd, Isner rallied to recover his losses and then took the tie-break as Youzhny sprayed a backhand narrowly wide.
The Russian secured a tight third set with an ace however, and his break in the third game of the fourth proved decisive.