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Del Potro finished with 77 winners to Nadal's 67 but failed to convert any of his five break points in the fifth set.
While Djokovic saw through Kei Nishikori with relative ease, winning the match in 4 sets 6-3, 3-6, 6-2, 6-2, Nadal played one of the best matches of the season so far as he prevailed in 5 sets over Juan Martin Del Potro, winning the match 7-5, 6-7, 4-6, 6-4, 6-4 in over four hours.
Having crashed out in the first round at Wimbledon for five consecutive times, Goerges' emotions spilled over at the end of the match after she embraced Bertens at the net.
"Rafa is a fighter", del Potro said. "Anything could happen", Nadal said.
While the Federer exit, to South African Kevin Anderson, losing 13-11 in the final set, is what will sadden most viewers and grab what there are of tennis headlines today, Nadal coming from two sets to one down against perennial almost man Juan Martin Del Potro produced perhaps the most unbelievable tennis of the day, and definitely the moment of the tournament.
The world number one, playing in his first All England Club quarter-final since finishing runner-up to Djokovic in 2011, then wasted four set points in the second.
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. The set stayed on serve until Del Potro secured the first break point for a 4-3 lead.
"It will be a different match that we played in Paris a few weeks ago", Del Potro told reporters.
"It´s not good for me".
"Obviously I'm very ecstatic to get through that match", Anderson said.
Del Potro trails Nadal 10-5 in head-to-head meetings - his five wins all coming on hard courts.
Eighth seed Anderson will play American ninth seed John Isner on Friday for a place in Sunday's final.
They have met on 51 previous occasions, but not at this stage of a Slam since the 2014 French Open semi-finals.
"Of course I'm sorry for Juan Martin".
"Very happy, a very important achievement for me to be back in the semi-finals of Wimbledon". But he blew those three set points, the last with a double-fault he later called "a big mistake".
Down two sets to love I tried my best to keep fighting.
Like Federer and Anderson, Nadal and del Potro Nadal slugged it out for more than four pulsating hours before Spain's 17-times major victor finally landed the knockout punch.