Nadal lost only eight games after dropping a first-set tiebreaker and secured his spot in the round of 16 with a 6-7 (3), 6-3, 6-1, 6-4 victory over Argentina's Leonard Mayer.
The Spaniard needed three hours, 15 minutes to finally dispatch Mayer, mainly due to his inability to cash in on a staggering number of break-point opportunities. Nadal had 25 chances to break the Argentine but converted only six times.
Mayer won the opening set in 63 minutes and managed to save each of the first 13 break points against him. Once Nadal finally broke through, the momentum quickly swung in his favor.
"When you see that you lost a set that you had triple more opportunities than your opponent, then of course you are in trouble," said Nadal. "At the beginning of the second, I had break points again. After that, finally I converted one at the 14th opportunity. After that, the match was completely different."
Standing between Nadal and the quarterfinals is a matchup against Alexandr Dolgopolov of the Ukraine on Monday. He said his latest win will help prepare him for what's ahead.
"You need matches like this," said Nadal. "Then now I have the opportunity to compete again, to try to do it well. I am in the second week. That's the important thing. I already won three matches in a row. That's important news for me."
The 24th-seeded del Potro blew past 11th-seeded Spaniard Roberto Bautista Agut 6-3, 6-3, 6-4 in the third round.
The 6-foot-5 Argentine hit 14 aces while collecting 38 winners to 32 unforced errors. He converted five of his 13 break points.
"I think I played the best match of the tournament," said del Potro, the 2009 U.S. Open champ. "I hit so well my forehand. I served well during the whole match. I played very smart with my slice. I came to the net very often, tried to be aggressive all the time, and I think I played well."
Thiem was equally impressive. The Austrian, who turns 24 on Sunday, got past Adrian Mannarino of France 7-5, 6-3, 6-4.
"I am pretty satisfied," said Thiem, who is looking to reach the U.S. Open quarterfinals for the first time. "It was way better than the first two rounds. I don't really like to play against him. He can hurt me or it's not really easy for me to get to my good shots against him, because he's playing flat.
"For sure, by far, the best performance by me."
Thiem trailed 3-5 in the opening set, then reeled off seven straight games to take control.
Monfils had injured his knee in his previous match, but when asked what caused him to retire in Saturday's match, he said, "The body. Whole body."
He later mentioned both knees, arm and back.
Goffin's next match will be against 19-year-old Andrey Rublev of Russia, who defeated Damir Dzumhur of Bosnia and Herzegovina 6-4, 6-4, 5-7, 6-4.
Philipp Kohlschreiber of Germany, the 33rd seed, advanced with a 7-5, 6-2, 6-4 victory over Australian John Millman, and Alexandr Dolgopolov of the Ukraine defeated Viktor Troicki of Serbia 6-1, 6-0, 6-4.
Third-seeded Roger Federer was slated to play his third round match on Saturday night.