But that all ended when the top-seeded player lost - 2-6, 6-7 (5), 7-5, 6-4, 13-11 - in a dramatic match that lasted more than four hours.
"I really tried my best to keep fighting", Anderson, 32, told the BBC immediately after coming off court from the 4-hour, 14-minute match. He was, after all, the runner-up at last year's US Open.
"If you go out there with doubts or unsure what's going to happen, like I maybe did a little bit in that first set, it's not going to go your way". "Beating Roger Federer here at Wimbledon will be one I remember, especially in such a close match", Anderson said. There's hopefully two more matches still to be played.
But he seemed to answer any question about whether he'd be addled by the unfamiliar environs or Anderson's massive serve in the first 26 minutes, closing the opening set with the impeccable form he'd shown in winning his first five matches without losing a set or his serve.
Nadal reached the quarterfinals of Wimbledon for the first time since 2011 after defeating Jiri Vesely in a 6-3, 6-3, 7-5 victory on Monday.
He was leading by two sets and 5-4 in the third when, with Anderson serving, he got to Advantage.
Federer faces eighth seed Kevin Anderson, who he has not dropped a set against in four previous meetings.
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We were happy, you weren't happy for us to be happy at that time, ' Wright said. "There's a lot we could have done better". Perisic was mightily unlucky not to add to his tally when his angled shot beat Pickford but cannoned off the post.
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Previously only Jo-Wilfried Tsonga had beaten Federer at Wimbledon after being two sets down, but the big-serving South African added his name to that list with one of the great SW19 performances.
And, despite his two-set advantage, the 20-times grand slam victor never looked entirely comfortable, despite having never previously lost a set to Anderson in four other meetings. Few considered Anderson as having a chance. Anderson leveled for 7-7, 8-8, 9-9, 10-10. And here at Wimbledon, there has been a quiet confidence about Anderson. But then fourth and fifth, obviously the fifth was long, that's like two sets, the fifth.
Federer, who was bidding to extend his record eight men's titles, was ousted Wednesday by free-hitting Kevin Anderson, who battled back from a two-sets-to-none deficit.
"It's just not one of my best days", he said.
"To be honest, I didn't feel mental fatigue. Obviously getting through it, I feel like I can take bigger steps".
Anderson will now rest ahead of Friday's final-four match. Federer may well be the greatest of all time but even he will find it tough to win at that age. He touched post-match on an injury-ravaged 2016, and how his coaching team and nearest and dearest put him back together.
Now, there is an ongoing mission to continue flying the South African flag in tennis. He knows attention will be on him from back home, and has spoken of his hope to be an inspiration for the next generation.