In a stark contrast from the fired-up atmosphere in his incident-filled match with Stefanos Tsitsipas, Kyrgios kept his focus on the court and ultimately won 4-6 6-4 7-6 (7-2) 3-6 6-2.
Kyrgios appeared to be struggling with a shoulder issue throughout the contest, and Nakashima needed just the one break in the first set at 5-4 before the physios came on for the Australian.
Even with his shoulder injury, Kyrgios managed to break early in the second set after a pair of Nakashima double faults and a shanked forehand, and the big-serving 27-year-old held to level proceedings.
The medical team would continue to make sporadic appearances as Kyrgios grimaced in pain throughout the closely-fought third set, but he raced away in the tie-break courtesy of a flurry of aces and a cross-court forehand winner.
Kyrgios would seemingly accept a fourth-set defeat with some low-effort returns, but the Australian dominated the fifth and took the first match point available to him.
De Minaur dominated the first two sets and would seemingly ease his way into the quarter-finals, but Garin responded brilliantly to win 2-6 5-7 7-6 [7-3] 6-4 7-6 [10-6].
Twenty-two-time Grand Slam winner Rafael Nadal would close the day on centre court against 21st seed Botic van de Zandschulp, and after ploughing through some nervy moments, the former came out on top 6-4 6-2 7-6 [8-6].
While serving for the match, Nadal did begin with an uncharacteristic double fault and found himself 0-40 against the Dutchman; despite saving one with an ace, a backhand slice straight after landed long to keep Van de Zandschulp's tournament alive that little bit longer.
Nadal also had three match points saved in the tie-break, but Van de Zanschulp misjudged a smash to send the Spaniard through to a quarter-final with Taylor Fritz, who saw off Jason Kubler 6-3 6-1 6-4.
Halep posted a magnificent 89% win rate on her first serves compared to just 46% for Badosa, and the 30-year-old is now the only previous major winner left in the women's tournament.
Before Halep stormed into the last eight, Elena Rybakina made a Grand Slam quarter-final for only the second time in her career by beating Petra Martic 7-5 6-2, and Alja Tomljanovic set up a tie with the 23-year-old after a 4-6 6-4 6-3 success over Alize Cornet.
The impressive run of France's Harmony Tan also came to an end in the last-16, as Serena Williams's conqueror was comfortably swept aside by Amanda Anisimova 6-2 6-3, which saw the 20-year-old American set up a quarter-final with Halep. body check tags ::