Anderson was sticking to his guns, though, and after saving match point the eighth seed secured another break of the Federer serve and snatched a set back.
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.
But, turning 37 in less than a month, Federer refused to blame fatigue after giving up a two-set advantage for the first time since doing so seven years ago against Jo-Wilfried Tsonga and Novak Djokovic at consecutive slams at Wimbledon and the US Open.
The 36-year-old had needed only 26 minutes to take the first set, leaving him horrified as a fifth successive Wimbledon semi-final slipped through his fingers from such a commanding position.
Sachin, who is a fan and friend of Roger Federer, has often attended Wimbledon clashes of the tennis star.
Beating Roger Federer here at Wimbledon will be one I remember, especially in such a close match.
Despite his anger, Djokovic still reeled off 10 of the last 12 games of the quarter-final.
After a marathon final set, a double fault on Federer in the 23rd game was ultimately what did in the No. 1 player.
When Anderson broke again in the fourth, Federer was suddenly on the ropes. Those are the kind of circumstances that you just have to accept.' He also revealed: 'Post-match I heard that the organisers were planning to cancel my match if Monfils and Anderson went to a fifth. I said today is going to be my day.
World number one Nadal, the two-time champion, reached his first quarter-final at Wimbledon since 2011 - when he went on to finish runner-up - with a 6-3, 6-3, 6-4 win over Jiri Vesely of the Czech Republic.
After an imperious Federer blew him away in the opening set, Anderson made things tricky for the Swiss legend in the second.
Three-time champion Djokovic, who hasn't won a Grand Slam since French Open in 2016, seems to have hit peak form at the right time.
"I don't think it's something anybody aims for, to win every match in straight sets".
'I don't think it really mattered, to be honest.
Federer couldn't convert a break point at 3-4 and as the final set headed into extra time a lone voice in the crowd, mindful of England's imminent World Cup semi-final against Croatia, shouted out "Hurry up I need to watch the football".