Kyrgrios produced some sublime tennis to secure a 6-7 (2) 6-4 6-3 7-6 (7) victory and knock the No4 seed out, but only after the match threatened to descend into chaos.
The enfant terrible of tennis had earlier demanded his opponent be defaulted after hitting a ball into the crowd, narrowly missing a spectator, initially refusing to continue playing until he was given a satisfactory answer from the umpire.
The 27-year-old also demanded a new line judge following one bad call and complained to spectators about another official before serving, at one point prompting Tsitsipas to walk back to his towel amid pantomime boos from the crowd.
The antics clearly got under Tsitsipas’ skin as twice he hit the ball straight at Kyrgios and also at the scoreboard.
The pair shared a cursory handshake at the end but Tsitsopas was in no mood to be civil 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 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.”
Additional reporting by Press Association and Reuters.