Anderson had already battled through another epic five-setter, defeating Roger Federer in the a quarter-final that ended 13-11 in the fifth set.
An Isner ace fittingly concluded the 12 games in the first, before Anderson recovered from a mini-break down to take a one-set lead after an hour and three minutes.
Anderson will now attempt overturn a losing record against both Nadal (5-0) and Djokovic (5-1). The Swiss was heading into the meeting as a favourite, he had not lost any set in his first four matches of the tournament.
In a final set that lasted almost 3 hours, Anderson had break points at 7-7, 10-10 and 17-17 before finally earning the decisive breakthrough to go 25-24 up - drawing a massive roar from the crowd.
Fast food chain Nandos, which originated from South Africa, has pledged to give away free meals to people who share names with the two players, until Anderson is knocked out of the tournament or wins the final.
Ultimately, it was Anderson who prevailed, taking the match 7-6, 6-7, 6-7, 6-4, 26-24.
After being kept on the run for six hours and 36 minutes, the longest ever singles semi-final at the All England Club, how the 32-year-old was still standing was anyone's guess.
Anderson had break points at 7-7, 10-10 and 17-17 before finally earning the decisive break - drawing a massive roar from the crowd.
It was a similar tale in the fourth set where the South African broke for 3-2 only to hand the break straight back.
Nadal and Djokovic will meet for the 52nd time.
Victory on Friday would put him in a sixth Wimbledon final and 25th at the majors. For us to be out there for that length of time.