The 144th-ranked Kyrgios, a wild-card entry, hit 37 aces and delivered a between-the-legs winner on one point. He is the first man to get to the quarterfinals in his Wimbledon debut in 10 years.
"You gotta believe that you can win the match from the start," Kyrgios said, per CBSSports.com. "He hit some extraordinary shots. That's what he's always going to bring."
He's also the first player ranked outside the top 100 to beat the No. 1 man since No. 193 Andrei Olhovskiy defeated Jim Courier at Wimbledon in 1992.
Nadal has appeared in five finals at the All England Club. But he lost in the second round in 2012 and the first round in 2013.
Last month, Nadal won the French Open title for the ninth time, and the fifth time in a row.