Anderson, the eighth seed, who made the US Open final previous year, broke the Isner serve twice in the fourth set to level the match.
Serena Williams goes for her eighth Wimbledon title and first Major championship since giving birth to her daughter, Olympia, on 1 September. "I was pretty close to making a Grand Slam final and it didn't happen".
With Anderson serving for the final at 25-24, Isner handed his opponent two match points when a return sailed long.
The South African was then on court for nearly seven hours as his semi-final tie with John Isner ended 26-24 in the final set.
Novak Djokovic was leading Nadal 6-4, 3-6, 7-6 (9) in a compelling showdown filled with entertaining points that was suspended as soon as the third set concluded at just past 11 p.m. local time, the curfew at the All England Club.
Second seed Nadal saved a break point at the start of the second set and celebrated holding serve with a trademark upper-cut fist pump.
Djokovic, meanwhile, is seeking a fifth final at the All England Club and 22nd at the Slams.
"It's hard to pick the words, I am just going through things that flash back - the last 15 months, everything I have been through to get here", said 12-times Grand Slam champion Djokovic, who has suffered a career-slump in the past 18 months.
"But I'm in the final of Wimbledon and it's an incredible achievement for me after what I've been through".
The final scorecard was 6-4 3-6 7-6 3-6 10-8 in Djokovic's favour.
The victor will face Kevin Anderson in Sunday's final. He reacted by getting broken again to trail 5-3 in that set by raising his left shoe and violently pounding his racket against it - one, two, three, four times.
"I hope this is a sign for (grand) slams to change this format out of five sets", Anderson told media in his postmatch interview (per thescore.com).
Anderson also played an extended fifth set in the quarterfinals, eliminating eight-time Wimbledon champion Roger Federer 13-11 in the final set.
Isner was a part of that one as well in 2010, beating Nicolas Mahut 70-68 in the fifth set after 11 hours, 5 minutes - the longest match at any tournament.
But only one of these men can move through to take on Anderson tomorrow, and they will resume today, when ticket holders for the women's final will get an unexpected treat.
"If one person can´t finish the other off before 12-All, then do a tiebreaker. I really do. I think with the performances I've had, I deserve to be in the semifinals", he continued.
Ever so slowly, having looked as if he might be swept away, Nadal worked his way back into the argument, and two sublime drop-shots - one sliced from the baseline, the second from short range - helped him to set-point in the tie-break, but he lost control of a backhand and they changed ends at 6-all.
The exhausted Anderson can only hope that another two sets of equal ferocity are required on Saturday.
Anderson was the runner-up to Rafael Nadal at last year's U.S. Open.