The 19-year-old, the youngest man in the draw, turned a remarkable Wimbledon main draw debut into a spectacular one, defeating the Spaniard 7-6 (7-5) 5-7 7-6 (7-5) 6-3 in just under three hours on Centre Court on Tuesday.
The world No.144 will face Canadian eighth seed Milos Raonic on Wednesday for a place in the semi-finals.
"I was in a bit of a zone out there, it hasn't sunk in yet," Kyrgios said.
"I played some extraordinary tennis. I was struggling a little bit on return but I worked my way into it and I got that break in the fourth set. I served at a really good level all throughout the match so I was really happy."
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Kyrgios says from the outset he had the self-belief that he could beat Rafael Nadal.
"You've got to believe you can win the match from the start and I definitely thought that."
"I'm playing some unbelievable tennis on the grass. And he hit some extraordinary shots and that is what he is always going to bring."
Kyrgios defies expectations in one of Wimbledon's biggest upsets
Kyrgios has became the first teenager to defeat a world No.1 at a grand slam since Nadal did it against Roger Federer at Roland Garros in 2005.
Sport commentator Steve Pearce is currently in London covering Wimbledon.
He says Kyrgios defied expectations in defeating 14-time Grand Slam winner, Rafael Nadal.
"Kyrgios had to play out of his skin and had to show incredible mental strength and resilience to achieve the result that he had. And he did it superbly," he told Sean Munaweera.
Kyrgios is the first player ranked outside the top 100 to defeat a world No.1 at a grand slam since Andrei Olhovsky defeated Jim Courier at Wimbledon in 1992.
Kyrgios also became the youngest man to reach the last eight at Wimbledon since compatriot Bernard Tomic in 2011 and the first to reach the quarter-finals on debut since Florian Mayer a decade ago.
Sports commentator Pearce says the win could signal a brighter future for Australian tennis.
"I've been here at Wimbledons recently when we have been bemoaning the worst Wimbledon ever for Australians since 1620 or something. This one is not going to go down like that. This one is going to go down as the breakthrough year of Nick Kyrgios. The bigger picture looks brighter as well."
Nick Kyrgios faces no. 8, Milos Raonic of Canada tomorrow. Pearce says the match is a difficult one to call.
"He [Milos] has got that big serve, that's going to be a difficult match to pick," he said.
"I think Nick's greatest challenge here - he has shown he can play...we know he can play, we know he can handle the big atmosphere but I think mentally, physically he would have put both of those energies into the [Nadal] match. And he has got to come back again tomorrow afternoon London time...it's a tough ask because this guy is a good player, but from what we've seen today he clearly can win."
Opponent Rafael Nadal congratulated Kyrgios on his win, warning him of the pressure to meet new expectations.
"Everything is a bit easier when you are arriving. Everything is new, nothing to lose. Everything is good, everything is postive. So we'll see if he is able to improve and play at very high level for a long period of time."
Prime Minister Tony Abbott has also said his congratulations.
Kyrgios wins in a four set nail-biting match
Far from overawed in the biggest occasion of his life, a free-swinging Kyrgios lapped it up, going toe-to-toe with the 14-times grand slamchampion in an enthralling encounter.
He served brilliantly - blasting 37 aces - reeled off a string of massive winners but also mixed up his game cleverly.
Perhaps most surprisingly, after making a superb start Kyrgios was able to maintain his level through the match.
After carving out an unlikely run to the last 16 on outside courts, Kyrgios - a wildcard entrant - was elevated to Centre Court status for the biggest match of his life.
Any questions over how the Canberra teen would handle the occasion were answered quickly and emphatically as he put on a serving exhibition in the first set.
The Australian lost only four points on serve for the entire set, none behind his first serve, as he smashed down 13 aces.
But his performance was far from one-dimensional, matching it with Nadal in the longer rallies and putting pressure on the Spaniard's serve.
He earned three break points let in the set, including a set point, but couldn't convert, however started strongly in the tiebreaker, racing to a 4-0 lead.
Nadal rallied but Kyrgios held his nerve, serving an ace to take an unlikely one-set lead.
Early in the second set Kyrgios had the crowd in awe with an outrageous, through-the-legs drop shot while down 40-0 on Nadal's serve, accepting the applause with his arms stretched wide.
Serving to force a second set tie break, some careless errors gave Nadal a sniff and the Spaniard converted his second set point to break the Australian's serve for teh first time.
The third set was another closely-fought affair but, just as the match looked to be swinging Nadal's way, Kyrgios again showed the nerve that has been a hallmark of his campaign.
He saved one set point before edging a tight tiebreak, needing just one set point to regain control of the match after a stunning cross-court return resulted in Nadal putting a backhand wide.
Nadal had lost the first set in his previous three matches and it seemed inevitable he would rally again in the fourth set.
However it was Kyrgios who struck first, securing a break to go 3-2 up.
He showed no signs of giving up his lead, and when given the opportunity to serve for the match, he didn't drop a single point.
Kyrgios fittingly sealed the historic win with an ace, raising his arms in joy, looking with disbelief to his support box and performing a dance.
"I didn't know what to do: I've just turned to everyone that's supported me my whole life. I didn't really know what that dance was."
High hopes from former coach
Tennis coach Andrew Bulley has high hopes for his former student following his stunning Wimbledon win.
While it’s the teen’s strong serve that’s captured the world’s attention, Mr Bulley said his former student’s success has a lot to do with his attitude.
“His mind is amazing, to be able to perform at that level,” he said.
“… That’s very mature for a young man. That’s really what sets him apart, that belief that he has in his game.”
Kyrgios will now face Canadian eighth seed Milos Raonic in the quarter-finals at Wimbledon, where Mr Buller believes the rising star will see more success.
“If he keeps his routine and keeps composure and keeps that belief he has in himself, the world’s his oyster,” he said.
