Second seed Nadal lost a mere seven points on serve in the first two sets, struck 37 winners and barely put a foot wrong, comfortably sealing a last-eight meeting with Juan Martin Del Potro or Gilles Simon.
That came at a key moment in the third set, which was a tougher examination of Nadal than the initial two.
Del Potro repelled them both but Rafa held at 15 in the following game, clinching the set 6-4 and sending this incredible encounter into a decider.
Nadal carved out the crucial break in the opening set for a 6-5 lead and claimed the opener off a Del Potro backhand error.
In one of the best games of the tournament, Rafa saved three break points in game eight to stay in front and he sealed the deal with a hold in game 10, setting the blockbuster semi-final clash with Novak Djokovic on Friday.
In the next set, Del Potro broke and served for the set at 5-4, but double-faulted and Nadal clinched the break-back with a forehand victor down the line for the second set to be decided by a tiebreaker.
The dogfight Nadal feared and Del Potro knew was his only route to the semi-finals had begun in earnest.
The fourth-round match resumed on Tuesday afternoon after bad light had stopped play on Monday with the Argentinian leading by two sets to one.
Nadal broke for 3-2 but had to save break points in the sixth and eighth games before securing a memorable victory.
"Against Rafa", del Potro said, "you must go for winners all the time". The hard-serving American beat Milos Raonic of Canada 6-7 (5), 7-6 (7), 6-4, 6-3 to set up a meeting with Federer's conqueror Kevin Anderson in the last four.
Simon saved a fourth match point when he threw the kitchen sink at a forehand return and he eventually took his fourth break point to level at 5-5.
"I do think that towards the end of the match there was a certain dampness in the sections where there was still grass, nearer the net, when the humidity drops", Nadal explained in his Spanish language press conference.