The two-time victor will meet Novak Djokovic in the last four on Friday.
A year after the epic encounter between Nadal and Djokovic at the semifinal stage of Roland Garros, they took on each other in the final in 2014.
But while Nadal and three-time champion Djokovic were expected to win, and Isner seeded to do so over Raonic, Anderson had never even extracted a set from Federer in four previous meetings.
"I'm really not thinking about being an underdog or being a favourite", he said.
Playing Djokovic was the sternest test and he came through a dramatic five-setter dubbed the greatest clay-court match of all-time by Bjorn Borg and John McEnroe. I just tried to fight for every point.
A sprightly Nadal went on the front foot to turn the tide in the fourth, Del Potro twice hitting the deck as he was broken to love to trail 3-2 and while he saved two set points behind his powerful serve, the 11-time French Open champion was jumping for joy after a searing backhand victor made sure the match would go all the way.
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"I am very happy the way that I survived a lot of important points in that fifth set", Nadal said. But if and when Djokovic does break serve, or win a set, or save a set point, or do something to fire himself up and sow doubt in Nadal's head, all of that could be turned upside-down in a hurry, the same way their rivalry has been turned upside-down in a hurry in the past.
The unforgiving match had sent Del Potro tumbling to the grass on more than one occasion.
While Nadal and Djokovic are old hands at winning Slams, the man stood on the opposite side of the net in Sunday's final will be bidding to win a first major.
That mishap could not stop Nadal from reaching his sixth Wimbledon semi-final and he celebrated the moment by raising both arms up into the skies after four hours and 48 minutes of thrilling action.
Anderson is the first South African to make the last-four since Kevin Curren in 1983.
"But my goal is to try to play very well". I'd guess that Rafa will have more self-belief than Djokovic in the early going.
QUOTE OF THE DAY: "I'm going to say hers because she's moving those feet now, she's walking, maybe a little too fast" - Seven-time champion Williams on whether she or her daughter Olympia has made greater improvements to their footwork in the last 10 months.