The 19-year-old beat the reigning French Open champion 7-6 5-7 7-6 6-3 as Nadal bid another early exit from the All England Club.
Kyrgios' defeat of Nadal represented the first time a player from outside the top 100 has beaten a world No.1 since 1992.
Nadal lost out in the first round in 2013 to Steve Darcis, a year after slumping to a second-round defeat at the hands of Lukas Rosol.
He performed unconvincingly in his three matches last week and on Tuesday was overpowered by the dynamic Canberra kid as his Wimbledon woe continued.
Kyrgios will face Canada's Milos Raonic in the last eight following his fourth round triumph.