Anderson, a 2017 U.S. Open runner-up, is now looking good going into the semifinal against either Canada's Milos Raonic or U.S. competitor John Isner.
"I just kept on telling myself I have to continue believing".
"I'm not quite sure what to say, I had to try my best to keep fighting", Anderson told the BBC. Anderson upset top seed Roger Federer of Switzerland on Wednesday.
"That's how important Wimbledon is to me and to us over here".
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.
Anderson is the first South African man to make the last four at Wimbledon since Kevin Curren in 1983. Watch Roger Referer vs Kevin Anderson live streaming online on ESPN TV this morning at 8 am EST / 5 am PST with a spot in the semifinals at stake.
Asked yesterday if he had concerns about noise from the Centre Court crowd, Federer light-heartedly replied: "I'm more concerned the World Cup final will have issues because the Wimbledon final is going on". That's my problem really'. "I had my chances and I blew it".
As a result, the Canadian's run at Wimbledon ended in the quarter-finals for the second year in a row.
Anderson put up a bit more resistance in the second and even became the first this Wimbledon to break Federer's serve. With Anderson serving, Federer held a match point at 4-5, 30-40 - but Anderson rallied back to win the game.
And then, slowly, over the next two-plus hours, all the way until the fifth set reached its 24th game, as the temperature dropped and the spectators' cries of "Let's go, Roger!" echoed through the shadows, everything came apart for the eight-time champion against an opponent who'd never beaten him before nor made it this far at the All England Club.
Federer shocked by Anderson in Wimbledon quarters epic
World number one Nadal faces a tricky test against power-hitter del Potro in his first Wimbledon quarter-final since 2011. Federer had been pursuing a 13th Wimbledon semi-final and a 44th appearance in the last four of a grand slam.