Nadal wasted three match points during his last-16 tie with Kyrgios.
Nadal, victor in Acapulco in 2005 and 2013, was playing his first event since falling in the Australian Open final to Novak Djokovic. On Tuesday night, the second-ranked Spanish star opened play with a 6-3, 6-3 victory over Mischa Zverev.
In conversation with his trainers, he said, "I'm gonna get booed off the court!"
Spain's Rafael Nadal plays the ball during his Mexican Tennis Open round 2 match against Australia's Nick Kyrgios, in Acapulco, Mexico, Wednesday, Feb. 27, 2019. "A tough day. But I'm not too sad about it". "The rule in the book says he has to play to the speed of the server, but Rafa has his speed every time [receiving or serving], so I'm not going to comment on him".
The world No.44 converted six break points and delivered the contest's only two aces to set up a quarter-final clash with third-seed John Isner.
Millman blitzed world No.87 Peter Gojowczyk.
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Interestingly, while Nadal is known on the circuit for his mental strength, in Thursday's match, it was what would prove to be his undoing.
Kyrgios eventually claimed an unforgettable 3-6 7-6 7-6 win after a rollercoaster three hours. Lesia Tsurenko, the women's victor the last two years, is skipping the event.
Kyrgios' impressive streak of winners and booming serves were overshadowed by late hostility that erupted between the pair when the match was on the line.
The Aussie's career record versus Nadal is now an even 3-3, but he faces a quick turnaround in the quarterfinals against another multiple Slam victor, Stan Wawrinka, on Thursday.
Another huge test awaits in the last eight in Wawrinka, who beat American seventh seed Steve Johnson 7-6 (7-5) 6-4 at the ATP 500 event played on hard-courts.
John Isner of the USA serves against Sam Querrey of the U.S.in their Mexican Tennis Open round 2 match in Acapulco, Mexico, Wednesday, Feb. 27, 2019.