Anderson won the first set 7-6 (8/6) before Isner claimed the next two, 6-7 (5/7), 6-7 (9/11) with the South African claiming the fourth 6-4 to level the semi-final.
As Isner and Anderson eclipsed 30 total games in the fifth set, Isner set a new Wimbledon record for most aces in a single tournament.
He finally broke the 33-year-old American in the 49th game of the decider after coming close in a couple of earlier games and looked impassive as he held his nerve to secure victory.
The reason the match went on for so long comes down to one of Wimbledon's quirks - a five-set match can not end on a tiebreaker, a tradition shared at the French Open and the Australian Open.
Because of the length of the first match, that semifinal will be played with the roof closed.
Anderson is trying to follow up his five-set win over Roger Federer in the quarterfinals, with both men appearing in their first semifinal at the All England Club. However, Melichar and Peschke won the next two games to seal it.
The 32-year-old Anderson will vie for the title on Sunday against the victor of the match between Nadal, the world No. 1, and three-time champion Novak Djokovic. Though Raonic outgunned Isner in that respect - 31 to 25 - he was unable to see through service games as convincingly.