Djokovic won 7-5 4-6 7-6 (7/2) 6-7 (6/8) 6-3 and now Andy Murray or Jerzy Janowicz stand in the way of a seventh grand slam title.
Nobody inside Centre Court could quite believe the match had reached a deciding set, which yet again began with both players holding serve.
The Serbian top seed had to dig deep in the fifth game to deny Del Potro, who was receiving attention during the breaks.
The Argentinian saved a break point in the following game, with some sloppy play from the world number one helping.
There were some astonishing rallies but Del Potro was visibly tiring and allowed Djokovic two break points, the Serbian converting the second for 5-3.
It allowed the top seed to serve for the match and, having saved a break point, he secured his place in the final, winning through in four hours and 44 minutes.
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