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 worn out player, to battle his way out of numerous 0-30 holes.
Second-seeded Rafael Nadal and 12th-seeded Novak Djokovic took the court after Isner and Anderson, about 8:10 p.m. local time.
Novak Djokovic (12), Serbia, leads Rafael Nadal (2), Spain, 6-4, 3-6, 7-6 (9), completion of suspended match.
They walked out under a closed Centre Court roof at around 8pm, with officials anticipating darkness will fall before their semi-final match is resolved.
The first semifinal at Centre Court, between No. 8 seed Kevin Anderson of South Africa and No. 9 John Isner of the USA, features two powerful servers with similar games who have a lot less star power and considerably fewer Grand Slam trophies, to say the least: The Nadal-Djokovic combined count is 29, including five at Wimbledon.
Nadal said: "It has been a great match - I think a fantastic level of tennis for both of us".
At 7-8 Nadal won a brutal 21-stroke rally with a smash, raising his arms aloft as the crowd roared, then saved a match point with a backhand dropshot that had an eye-bulging Djokovic sprawling across the turf. "As I say the other day against Del Potro, anyone could win".
In the ensuing game, Anderson held serve one last time and clinched the victory when an Isner mishit drifted wide. Finally, at 24-24, Isner went down 0-40 and with his legs wobbling, Anderson finally broke on his second chance.
When asked how he would recover from such an epic and play in the Wimbledon finals on Sunday afternoon, the South African said: "It's tough, I really don't know". Anderson broke Isner's serve for the first time in 110 service games at Wimbledon earlier in the set.
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"But yeah, knowing that, maybe would be better if they play us first at 1:00, that's all".
While Nadal hasn't really been off the scene at all, Djokovic is ending a string of five straight majors in which he didn't play a semifinal match - his longest such stretch since 2006.
Nadal will regret his missed opportunity the night before, when he was in the ascendancy but passed up two set points.
Not to be outdone, Anderson had 49 aces of his own in the match vs. Isner.
"It's been a rollercoaster ride for him but he had a day off".
"But I'm in the final of Wimbledon and it's an incredible achievement for me after what I've been through". A few days' rest, maybe more than that, and I'll recoup and try to get all healed up again.
The eagerly-awaited confrontation between world number one Nadal, the champion in 2008 and 2010, and Djokovic, the victor in 2011, 2014 and 2015, only started after 8pm (1900GMT) on Friday. Marin Cilic beat Sam Querrey in that 2012 third-round match.
"John is a great guy and I really feel for him".
In a match between two of the game's biggest servers, Anderson started the match with a double-fault. The US Open is the lone major that has a tiebreak in the deciding set.