A deft lob helped Nadal take the first game of the second set, before each player held serve.
"Sorry to Juan Martin, he´s an incredible opponent and player".
Del Potro was in danger of being dragged into a fifth set when he squandered four match points, one with a double-fault, at 5-4 having hit back from 1-3 down.
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'Friday is another important match against opponent that is one of the most hard ones that you can face, ' he said after beating Del Potro.
When the 4 hours, 48 minutes of diving across the grass and leaping into the stands, of slipping and sliding, of so many moments of great tension - and, above all, great tennis - were done, when Rafael Nadal had sealed his Wimbledon quarterfinal victory, the man he edged, Juan Martin del Potro, was face-down at a Centre Court baseline.
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.
Nadal had three set points to go up two-sets-to-love earlier in the match.
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But back came Nadal to level before an enthralling final set which was punctuated by great shot-making and spectacular dives and falls by both players. Of course, have been an emotional match.
It was such a tense affair, particularly the 71-minute deciding set, that when it was all over, Del Potro lay on the ground, face down, and only got up when he saw Nadal standing over him.
Simon saved a fourth match point when he threw the kitchen sink at a forehand return and he eventually took his fourth break point to level at 5-5. "But Rafa cames to me and we made a big hug, and it was kind of him". My body feels okay. But I know a semi-final is one of those matches where anything can happen.
While Nadal's rivalry with Roger Federer may be considered as the most engaging, it is the Spaniard's rivalry with Djokovic which is the most enduring.
"I felt like it was getting better and better as time went on".
The second semi-final will see Nadal line up against former world number one and three-time Wimbledon champ Novak Djokovic.
Nadal saved three break points before an imperious forehand victor put him 5-3 up and he put away a simple volley to finally finish off Del Potro, then made his way around the net to embrace his tired opponent as he lay on the court following another tumble.