Anderson finally broke Isner on the 13th attempt in the fifth set and then held serve in the following game to wrap up the victory in six hours and 36 minutes, reports Efe.
The match began as expected with neither player able to earn a single service break over the first two sets.
The 6-foot-8 South African took the opener after saving one set point in the tiebreaker, finishing it off when Isner hit a forehand into the net.
The second set also came down to a tiebreaker, but this time it was the American who came out on top when he threw down an ace on the final point.
The third set appeared to mark a key turning point in the match, with Isner rallying from a break down and then also coming back from a mini-break down to win the tiebreaker after Anderson committed a costly double fault on set point.
But the South African showed no sign of discouragement and was also the fitter player on Friday even though he had had to play more than four hours on Wednesday in a 2-6, 6-7 (5-7), 7-5, 6-4, 13-11 upset of Swiss eight-time champion Roger Federer.
He won the fourth set despite once again squandering a service-break lead and appeared to have the edge heading into the decider.
Although both players had shown an ability to make inroads on their opponent's serve, the fifth set turned into a marathon featuring one service hold after another.
Anderson clearly had the edge though, as he did not have to face a single break point in the final set and forced Isner, who was clearly looking like the more fatigued player, to battle his way out of numerous 0-30 holes.
Finally, the South African broke through in the 49th game of the set when Isner lost serve by dumping a backhand into the net.
In the ensuing game, Anderson held serve one last time and clinched the victory when an Isner mishit drifted wide.
The match clocked in as the second-longest in Wimbledon history, topped only by Isner's epic 6-4, 3-6, 6-7 (7-9), 7-6 (7-3), 70-68 victory over Nicolas Mahut in the 2010 edition of the tournament, a match that lasted 11 hours and five minutes and was played over three days.
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