Anderson achieved something only Jo-Wilfried Tsonga and Novak Djokovic had done before as he fought back to prevail, 2-6, 6-7 (5-7), 7-5, 6-4, 13-11, in a thriller that lasted four hours and 13 minutes on No.1 Court.
It was Federer's earliest departure from Wimbledon since his shock second round defeat against Sergiy Stakhovsky in 2013.
"Down two sets to love I tried my best to keep fighting".
The World Cup showpiece will take place on Sunday at 18:00 (local time), which is 16:00 BST, meaning it is likely to kick off during the men's grass-court final, which eight-time champion Federer is a heavy favourite to be a part of.
"I just kept on telling myself I have to continue believing".
"It would take an unbelievable serving performance and for Roger had a bad serving day to cause an upset". That's the mindset you need against someone like Roger.
"The more I can just treat it like another tennis match, the better for me". "Matches likes that are very special".
However, Federer was unable to break his own record after dropping the third set as Anderson embarked on a courageous fightback.
It was a surprise result that now sends the eighth-seeded Anderson to the semifinals at Wimbledon, his first time making it that far in the storied competition that Federer has won eight times, including previous year.
Anderson never had made it beyond the fourth round at Wimbledon until this week, carried by his booming serve. "Knowing the four times they've played, Kevin hasn't got to him or seen any weaknesses from Federer, so that's a hurdle". This will be Djokovic's first semifinal at a major since the 2016 French Open when he completed the career Grand Slam.
Tendulkar, the former India captain widely renowned as one of the greatest batsmen of all time, was impressed by Federer's form after the 20-time Grand Slam champion was spotted praticising his forward defence during his victory over Adrian Mannarino at Wimbledon.
"I will watch Wimbledon from home, hoping for Rafa's win", Toni added. The match was played there after Novak Djokovic, having played three of his opening four matches away from Centre Court, had his request to play in the main stadium granted.
The 32-year-old certainly has nothing to lose, and can come out swinging - even breaking serve for the great Roger Federer may well be a test of patience and perseverance.
Djokovic looked in control in the first set.
But Anderson was just getting started.
Federer was completely out of sorts by now and his uncharacteristic struggles on his forehand didn't improve in the fourth set.
"He was down match point in the third set, and he's through to his first ever semi-final here at Wimbledon now".