Anderson had a break and set point chance at 5-4, but Isner fired down a gutsy 129mph unreturned second serve to keep himself in contention.
Anderson took a medical timeout after the third set.
However, Isner was then unable to convert a set point of his own in the tiebreak before 32-year-old Anderson wrapped it up thanks to a netted return.
In a match full of booming serves and countless aces, the first three sets were all decided on tie-breaks.
The players split the first four sets, three of them by tiebreaks.
As Isner served for a 16-15 lead, the match became the second-longest Wimbledon singles clash at just over five and a half hours. He has reached a career-high in the rankings and on Wednesday he defeated Canadian Milos Raonic in the Wimbledon quarterfinals, advancing the furthest he ever has in a Grand Slam tournament.
It was a similar tale in the fourth set where the South African broke for 3-2 only to hand the break straight back.
Isner is best known to many fans, particularly in Great Britain, for his astonishing contest with Nicolas Mahut on Court 18 at Wimbledon in 2010.
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.
A full but slightly tired Centre Court crowd geared up for a long decider, and on and on and on it went until, after six hours and 35 minutes, Anderson sealed his place in the final.
Isner, 33, a native of Greensboro, N.C., and Anderson, 32, who was reared in Johannesburg, were longtime rivals at the top ranks of college tennis, when Isner played for Georgia and Anderson, for IL.
Isner's semifinal match is scheduled for 7 am Dallas time on Friday and can be watched on ESPN. On the pro tour, Isner held the decided edge in their matches with an 8-3 record.
After taking out Roger Federer in remarkable fashion, 2017 US Open runner-up Anderson was forced to go the distance once again and he triumphed in remarkable fashion.
Nadal and Djokovic will battle for Sunday's final on the same court at 4pm.