The outspoken Kyrgios has made plenty of headlines so far at Wimbledon, and had to battle hard against 20-year-old American Nakashima on Centre Court on Monday, two days after his ill-tempered clash with Stefanos Tsitsipas.
That win over the world number five took four sets, but Kyrgios needed all five this time around, eventually prevailing 4-6 6-4 7-6 (7-2) 3-6 6-2.
The victory sent Kyrgios into the last eight at Wimbledon for the second time, after he reached the same stage by beating Rafael Nadal in 2014, while it is only the third time in the Australian's career that he has progressed to a grand slam quarter-final, having last done so in Melbourne in 2015.
It also kept up Kyrgios' 100 per cent record of winning Wimbledon matches that have gone to five sets, with the 27-year-old now 6-0 in that regard, with two of those victories coming at this year's edition of the major.
"First I want to say hell of an effort from Brandon, he's 20 years old and he's going to do some special things that's for sure," said Kyrgios, who needed medical attention on a shoulder injury during the tie, in his on-court interview.
"[It was] nowhere near my best performance, but I fought through, the crowd were amazing.
"I have played a lot of tennis in the last month and a half. His level didn't drop. My five-set level is pretty good and I've been here before, done it before and that is what I was thinking about."
The only disappointment from Kyrgios' point of view was missing out on an all-Australian quarter-final against Alex de Minaur, who squandered a two-set lead as he went down 2-6 5-7 7-6 (7-3) 6-4 7-6 (10-6) to Cristian Garin, who became the first Chilean player to reach the last eight of a grand slam since Fernando Gonzalez at the US Open in 2009.
Any nerves are nothing that a stiff drink will not fix for Kyrgios, however.
"I was really excited to play De Minaur to be honest, he's been flying the Aussie flag for so long and he was two sets up when I came on court," he said.
"I need a large glass of wine tonight for sure.
"I stepped out here amongst the greatest of all time and I beat Nadal [in 2014]. All these experiences that I've had got me over the line today."