In a match lasting three hours and three minutes, Kyrgios saved six break points and three match points before knocking out the top seed.
It was Kyrgios’ third win over Nadal in their six meetings and his antics on the court, including hitting an underarm serve, clearly rattled the world number two.
At the end of the match, the handshake between the pair was extremely frosty with Nadal barely looking in Kyrgios’ direction.
Kyrgios then took in the boos and applause from the Acapulco crowd.
In his post-match press conference, Nadal lashed out at Kyrgios saying: “He is a player who has ginormous talent.
“He could win Grand Slams and fight the top positions of the ranking, but there is a reason why he is where he is.
“He lacks respect for the public, the rival and towards himself.”
But Kyrgios did hit back at Nadal in his own media briefing saying: “I’m different, Rafa’s different, he can focus on what he needs to do.
“He doesn’t know the journey I’ve been through, he doesn’t know anything about me so I’m not going to listen at all.
“It’s the way I play, it’s the way he plays. He’s very slow between points. There’s a rule in the books that says you have to play at the speed of the server, Rafa has the speed every time.
“I’m not going to comment on his game, he has his game, I have my game.
“He played well, that’s the sport, people are different so I’m not going to take it [Nadal’s comments] into consideration at all.”
And in a post on Instagram, Kyrgios took a further jab at Nadal.
Kyrgios shared a clip of the match point and two pictures of himself with the caption: “Don’t doubt yourself, there are plenty of people who will do that for you.
“I can smell the blood when I play this dude #Emotions.”
Kyrgios will play Stan Wawrinka in the quarter-finals on Thursday.