After playing his worst game of the match, Djokovic then played his best, breaking Nadal with a fabulous cross-court passing shot to get the set back on serve.
Both players had set points on their own serve, and both were denied until Anderson scooped a forehand wide and Isner was ahead.
"The effort they both put in and the performance and the guts, the way they competed - a lot to be proud of", said Justin Gimelstob, one of Isner's coaches.
Others called for a rule change, suggesting a deciding fifth-set tie-break be introduced rather than waiting for a clear victor.
At least Anderson can boast of one runner-up finish, and it was recent, against Nadal at last year's U.S. Open.
The three-time Wimbledon remains the only player on the ATP Tour capable of defeating the pair on their favoured surfaces and he relished the cooler conditions.
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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.
John Isner could barely run after an exhausting battle with Kevin Anderson who beat the American 7-6 (8/6) 6-7 (5/7) 6-7 (9/11) 6-4 26-24.
This one seems rather tidy by comparison: Anderson won 7-6 (6), 6-7 (5), 6-7 (9), 6-4, 26-24. And now he's lost the second-longest one ever played at the All England Club.
He fashioned three break points from the next rally and took the second, the first break of the set.
Anderson weighed in with 49 aces to reach 172 so far. "We want to see Rafa!"
Almost three punishing hours later they both left Centre Court with their title hopes still intact.
Djokovic had two break points when Nadal was serving for the set, angrily remonstrating with himself when he failed to convert them before gifting the Spaniard the set with a backhand error.
"I like the level of tennis that I'm playing on right now". But Anderson roared back, outlasting the great Swiss to win 2-6 6-7 7-5 6-4 13-11.
"For us to be out there this length of time - I mean, not just on us, but coming back trying to compete at this sort of stage, going through this - it's happened to John before, when he's played another five hours".