Federer had a match point at 5-4 in the third set, but Kevin Anderson-the 6-foot-8 ball smasher from South Africa-saved that break point and went on to win the set.
Kevin Anderson told South African youngsters to "stick to their dreams" and follow in his footsteps after he knocked Roger Federer out of Wimbledon on Wednesday. Anderson held for 5-all, broke to 6-5 with a violent return victor off a 97 miles per hour second serve, then staved off three break points and closed the set with a 133 miles per hour ace.
Should Djokovic, Nadal and Federer win, it would be the first time all three played in a semifinal since the 2012 French Open.
Eighth seed Anderson will play 2016 runner-up Milos Raonic or American ninth seed John Isner on Friday for a place in Sunday's final.
"I kept telling myself to keep believing".
"Obviously I'm very ecstatic to get through that match", 32-year-old Anderson said.
In the end, it just wasn't meant to be Roger Federer's year at Wimbledon. "It's not the first time for me in the semifinals, but it is a win that I want to enjoy before I focus on the semis", he said.
It is the second time that 20-times Grand Slam champion Federer has lost at Wimbledon from two sets ahead, suffering the same fate against Jo-Wilfried Tsonga in the 2011 quarter-finals.
When Anderson broke in the second set it was the first time the Swiss had dropped serve at this Wimbledon.
"It would take an unbelievable serving performance and for Roger had a bad serving day to cause an upset".
Federer found himself scheduled on Court One having been ousted from his usual Centre Court domain for the first time in three years.
"I don't think it really mattered, to be honest". Every time I come back here, I try to be like them, so it's nice to be here. "I had my chances and I blew it". "Of course, it's important for me to be in these quarter-finals".
While Federer started out strong, besting Anderson 6-2 and 7-6 in the first few sets, his dominance became less complete as play went on.
Djokovic wrested back the momentum for good after coming from 0-40 down at 2-2 in the third set to hold serve, and then breaking his Japanese opponent in the next game.
Anderson never had made it beyond the fourth round at Wimbledon until this week, carried by his booming serve.
It was Federer who faltered at 11-11, double-faulting to hand Anderson a break point which he converted when the defending champion's tired forehand smacked 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.