Nadal, in the quarter-finals for the first time since finishing runner-up to Novak Djokovic in 2011, carved out the crucial break in the opening set for a 6-5 lead and claimed the opener off a Del Potro backhand error.
Djokovic's fall from grace found him ranked at 21st in the ATP World Rankings before the start of the tournament, but his path back to the top is being cleared, and he will face this year's French Open champion Nadal for the 52nd time in the pairs career.
The 17-time Grand Slam champion was not to be denied a place in the semis, though, coming through a monumental battle with the fifth seed to win 7-5, 6-7 (7), 4-6, 6-4, 6-4 in four hours and 47 minutes.
It was a breathless Wimbledon contest that kept on giving for nearly five hours - diving volleys, ferocious forehands, blazing backhands and even acrobatic tumbles - and at the end of it all Rafael Nadal was the one left standing on Wednesday.
The following year, Nadal downed the Serb, who was world number one at the time, 6-4, 3-6, 6-1, 6-7, 9-7 in the semi-finals in Paris, this time in four hours and 37 minutes.
World number one Rafael Nadal says he will have to be at his very best when he faces Novak Djokovic in Friday's much-anticipated Wimbledon semi-final.
"But is impossible to win always, even for him (Federer)".
Del Potro finished with 77 winners to Nadal's 67 but failed to convert any of his five break points in the fifth set.
Donald Trump shares letter from Kim Jong Un, says ‘progress being made!’
Both sides were expected to discuss the timeline and ways in which remains of American soldiers would be returned at the meeting. In a post on Twitter, Mr Trump said the letter, dated July 6, was very nice and was a sign of " Great progress being made! ".
Nadal was knocked out in the fourth round, losing 13-11 in the final set to Luxembourg journeyman Gilles Muller.
Nadal and Djokovic have faced each other 51 times in total with the Serbian shading it with 26 wins but the Spaniard has won their last two meetings.
"For the rest of the things, great news, semi-finals of Wimbledon again". Sometimes you play your best tennis and it's not enough to beat him.
The twice champion broke back but squandered four set points in the second set tiebreak, with a double fault on one of them.
Playing Djokovic was the sternest test and he came through a dramatic five-setter dubbed the greatest clay-court match of all-time by Bjorn Borg and John McEnroe.
Anderson is the first South African to make the last-four since Kevin Curren in 1983.
A few hours earlier, however, it looked as if it was going to be 32-year-old Nadal who would end up down and out.
The two have played some memorable matches over the years.
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