South African Kevin Anderson's hopes looked forlorn as Federer skipped through the opening two sets on Court One with his usual panache, but he turned the match on its head to cause the biggest shock yet in a tournament full of upsets.
Kevin Anderson produced an astonishing fightback from two sets down to beat eight-time champion Roger Federer 2-6 6-7(5) 7-5 6-4 13-11 in a quarter-final cliffhanger at Wimbledon on Wednesday.
The South African's hopes looked forlorn as Federer skipped through the opening two sets on Court One with his usual panache, but he turned the match on its head to cause the biggest shock yet in a tournament full of upsets.
It was his first win against Federer at the fifth attempt and means he is the first player representing South Africa to reach the semi-final here since Kevin Curren in 1983.
Eighth-seed Anderson, 32, saved a match point in the 10th game of the third set and grew in confidence against an increasingly-ragged Federer who had won the first set in 26 minutes.
He won the third set to snap Federer's 34-set winning streak at Wimbledon, and Federer was clearly shaken as Anderson dominated the fourth set to drag the 20-times Grand Slam champion into a decider.
Six times Anderson was required to hold serve to stay alive and each time he was equal to the task.
Federer eventually cracked at 11-11, double-faulting to hand Anderson a break point that he converted when the defending champion hit a weary-looking forehand halfway up the net.
Anderson stayed cool and sealed victory on his first match point with a powerful first serve which Federer could only return into the tramlines.
He will come up against another big hitter in the semi-finals -- American John Isner.
Isner reached his first Grand Slam semi-final as he beat Canadian Milos Raonic 6-7(5) 7-6(7) 6-4 6-3 in a clash of the giants at Wimbledon on Wednesday.
The 33-year-old saved a set point in the second set tiebreak to avoid going two sets down and then took control of the match to continue his dream run at the All England Club after years of unrewarded toil on the grasscourts.
Ninth seed Isner has taken 41 Grand Slams to reach his first semi-final -- one less than compatriot Sam Querrey who reached the milestone a year ago at Wimbledon.
It was a case of down but definitely not out as a Rafael Nadal kept picking himself off a slippery and dusty Centre Court surface to storm into the Wimbledon semi-finals with a pulsating 7-5 6-7(7) 4-6 6-4 6-4 over Juan Martin del Potro.
Just 90 minutes after defending champion Roger Federer was sensationally knocked out by South African Kevin Anderson on Wednesday, it seemed as if the grasscourt major would lose its top two seeds as Argentine Del Potro took a two-sets-to-one lead.
It was not as if Nadal was playing badly as he had lost only nine points on serve before heading into the ninth game of the second set.
But just before that game started, Federer's shock demise was flashed up on the giant on-court scoreboard and it was as if that threw the Spaniard off his stride and he fluffed his lines to drop his serve.
After Nadal squandered four set points in the third set tiebreak, with a double fault on one of them, Del Potro made him pay as he pounced on his first chance to raise the prospect of another astonishing upset on day nine of the championships.
But the second seed stayed alive by taking the fourth set before the gripping drama continued in an electrifying deciding set in which both players were left diving after volleys and slipping over as they chased after blinding winners.
Nadal ended the four hour and 48 minute thriller with a backhand volley winner past a lunging Del Potro who ended the contest lying flat on his stomach.
Next up for the Spaniard is a blockbuster last four showdown with Serb Novak Djokovic.
Three times Wimbledon champion Djokovic was a man on a mission after the former world number one beat Japan's Kei Nishikori 6-3 3-6 6-2 6-2 on Wednesday to reach the semi-finals for the eighth time.
"I feel like I'm peaking at the right moment," declared the 12th seeded Serb after joining Americans John McEnroe and Pete Sampras in fourth place on the list of most Wimbledon semi-final appearances in the Open Era.
The 31-year-old will play either second-seeded Spaniard Rafael Nadal or fifth-seeded Argentine Juan Martin del Potro in the last four.
Djokovic had looked in control after the first set on a sunny Centre Court but lost his cool and concentration in the second after a heated exchange with umpire Carlos Ramos.
With his 24th seeded opponent saving three break points to hold serve at 2-1, Djokovic bounced his racket off the baseline in frustration and then seethed after he was given a code of conduct warning.
"You think I ruined the court for just throwing my racket (down)? Do you think that or not? Be honest." the Serb exclaimed, shaking his head.
Nishikori promptly broke serve and then held to go 4-1 up before levelling the match at 1-1 but any sense of a fightback, and the possibility of a first Japanese man in the Wimbledon semi-finals since 1933, was short-lived.