Kyrgrios produced sublime tennis to secure a 6-7 (2) 6-4 6-3 7-6 (7) victory and knock out the number 4, but only after the match threatened to fall into chaos.
The enfant terrible of tennis had previously demanded that his opponent be given notice of default after hitting a ball into the crowd, narrowly missing a spectator, initially refusing to continue playing until he got a satisfactory answer from the referee.
The 27-year-old also demanded a new linesman after a poor call and complained to onlookers about another official before serving, at one point asking Tsitsipas to return to his towel amid pantomime anger from the crowd.
The antics clearly got under the skin of Tsitsipas, as he hit the ball twice right at Kyrgios and also at the scoreboard.
The pair shared a fleeting handshake at the end, but Tsitsopas was in no mood to be polite at his post-match press conference.
He told reporters: “It’s constant bullying, that’s what he does. He bullies the opponents. He was probably a bully himself at school.
“I don’t like bullies. I don’t like people who put other people down.
“He also has some good qualities in his character. But he also has a very bad side about him, which if exposed, it can really do a lot of harm and bad to the people around him.”
Additional coverage by Press Association and Reuters.