Kyrgios recovered from one set down to post an impressive 6-7 (2-7) 6-4 6-3 7-6 (9-7) win over the No.4 seed, setting up a Round of 16 tie with Brandon Nakashima with a scintillating performance on No.1 Court.
But the contest was not without controversy, with Kyrgios frustrating Tsitsipas by calling for him to be defaulted after the Greek narrowly missed a spectator when firing a ball into the crowd at the end of the second set.
The Australian then labelled the umpire a "disgrace" during an extraordinary outburst, and his antics seemed to get under the skin of Tsitsipas, who was deducted a point for sending another ball towards the spectators before appearing to hit a couple of shots directly at Kyrgios.
While Kyrgios praised his opponent – with whom he played doubles at Wimbledon three years ago – as "a hell of a player" in his post-match interview, neither player was in the mood for niceties in their respective news conferences.
First up was Tsitsipas, who accused Kyrgios of "constant bullying".
"That's what he does," the world No.5 said of his rival. "He bullies the opponents. He was probably a bully at school himself.
"I don't like bullies. I don't like people that put other people down.
"He has some good traits in his character, as well. But he also has a very evil side to him, which, if it's exposed, it can really do a lot of harm and bad to the people around him."
Kyrgios, who has now claimed four wins in five career meetings with Tsitsipas, responded to that criticism shortly thereafter, alleging the Greek was not popular in the locker room and saying his inability to handle such matches would hold him back.
"He's that soft, to come in here and say I bullied him? That's just soft," Kyrgios said.
"We're not cut from the same cloth. If he's affected by that today, then that’s what's holding him back, because someone can just do that and that's going to throw him off his game like that. I just think it's soft.
"I don't know what to say. I'm not sure how I bullied him.
"He was the one hitting balls at me, he was the one that hit a spectator, he was the one that smacked it out of the stadium.
"I didn't do anything. I was actually like … apart from me just going back and forth to the umpire for a bit, I did nothing towards Stefanos today that was disrespectful, I don't think. I was not drilling him with balls.
"I feel great, the circus was all him today. I think if he's making that match about me, he's got some serious issues, I'm good in the locker room, I've got many friends, I'm actually one of the most liked [players]. I'm set.
"He's not liked, let's just put that there. I'm good, I feel good."
Kyrgios is just one win away from matching his best run at Wimbledon, having reached the quarter-finals in 2014 with a win over Rafael Nadal before being beaten by Milos Raonic.