With world number one Rafael Nadal waiting for the victor, Tuesday's fourth set, played in much cooler conditions than the first three the day before, turned into a mini-epic before Del Potro eventually prevailed 7-6 (1) 7-6 (5) 5-7 7-6 (5).
Nadal fought back, from two sets to one down, to somehow defeat fifth seed Del Potro, who served 33 aces, 7-5, 6-7 (7), 4-6, 6-4, 6-4 in four hours and 52 minutes - the longest match of this year's tournament.
The Argentine next faces two-time champion Rafael Nadal, who has reached the Wimbledon quarterfinals for the first time since 2011.
There's no doubt Djokovic will be the fresher of the two when they meet on Friday, after Del Potro took a lot out of Nadal. And so it proved in a match that got better the longer it went as he ground out a 7-5, 6-7 (7), 4-6, 6-4, 6-4 win in four hours and 47 minutes, the longest of the tournament.
Del Potro finished with 77 winners to Nadal's 67 but failed to convert any of his five break points in the fifth set.
But Nadal was first to break in the deciding set and he built a 5-3 advantage with a looped forehand victor before confirming his final four place with a volley after four hours and 48 minutes. Del Potro broke and served for the set at 5-4, but double-faulted and Nadal clinched the break-back with a rasping forehand down the line.
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"In the end the court was a little bit slippery because the sun goes out and it was humid on the grass", Del Potro added.
'In the third set he started to play better from the baseline and I had couple of mistakes with the game I lost.
The dogfight Nadal feared and Del Potro knew was his only route to the semi-finals had begun in earnest.
The deciding fifth set was a tight battle, but in the fifth game, Nadal got the solitary break to lead 3-2.
"Rafa is a fighter", del Potro said.