The two big-hitters fought for more than six-and-a-half hours in the second-longest Wimbledon singles match of all time before Anderson finally got the all-important break to win an incredible final set 26-24.
Anderson, who was also involved in a five-setter in the quarter-finals when he came from two sets and match point down against Roger Federer, will now face either Rafael Nadal or Novak Djokovic in the final.
It was no surprise to see both players dominate on their own serve throughout, and even the first three sets took an average time of more than an hour to complete before the final set went on for almost three hours.
Isner had the chance to change things when he squandered three break points as early as the third game of the match, while Isner also let a set point slip through his grasp in the 10th game of the opener.
Instead it went to a tie-break - as did the following two sets - with Anderson winning the first of those but Isner winning the next two to put himself in control of the match.
The first two occasions on which Anderson did manage to break his opponent, Isner hit back immediately in kind, but a second break for the South African in the fourth set took it to 5-4, and he served it out to take the match to a decider.
It was a deciding set which would take almost three hours to conclude, with neither player dropping serve until the 49th game, when Anderson finally made the breakthrough.
The number eight seed then only needed one match point to wrap up the victory, booking his place in just the second Grand Slam final of his career.