A sprightly Nadal went on the front foot to turn the tide in the fourth, Del Potro twice hitting the deck as he was broken to love to trail 3-2 and while he saved two set points behind his powerful serve, the 11-time French Open champion was jumping for joy after a searing backhand victor made sure the match would go all the way.
First, on Wednesday he'll take to the court for a third consecutive day amid concerns over his fitness.
Nadal advances to his first Wimbledon semifinal since 2011.
Djokovic and Nishikori will play the first match on Centre Court, followed by arguably the pick of the quarter-finals between Nadal and Juan Martin del Potro, meaning Federer must make a rare visit to Court One.
Friday's other semi-final pitches Anderson, the eighth seed who lost to Nadal in last year's US Open final, against ninth-seeded American John Isner.
He reached the semifinals at the All England Club in 2013, but four wrist surgeries - three on the left - nearly made him retire.
Victory secured, Nadal climbed over the net and ran over to the baseline to help the distraught Del Potro back to his feet. I just tried to fight for every point.
The only fourth-round contest to be carried over to Tuesday lasted 4 hours, 24 minutes, making it the longest men's singles match of the tournament.
Given the fact he withdrew from a pre-Wimbledon event with a groin concern and called the trainer during his match with Simon, Del Potro's fitness could be a factor. I'm sure he's in good shape again. Del Potro said. "My body feels OK".
Nadal, the No. 2 seed, won the first set before dropping the second to his Argentine counterpart.
World number one Nadal, the 2008 and 2010 champion at the All England Club, trails Djokovic, the 2011, 2014 and 2015 victor, 26-25 in a rivalry which began at Roland Garros 12 years ago.
The South African is through to the last eight for the first time, and he said: 'Playing somebody like Roger Federer is going to be a great experience.
Stretching back to a year ago, Federer has won 32 consecutive sets at Wimbledon and will break his previous longest streak of 34 if he wins in straight sets. Raonic hit 31 aces to Isner's 25 but was broken three times, including the last game of the match.
Both players said the match is likely to come down to a few crucial points, but took different tones when asked to suggest where they might have an advantage.