Kyrgios, 27, had his racket smashed after losing the opening set and later locked up with the umpire after suffering a time foul for taking too long between points.
The Australian continued screaming from his chair, arguing that he needed to wipe his hands before playing.
“He said I was playing very slowly and statistically speaking I’m one of the fastest,” Kyrgios told reporters after reaching the quarter-finals in Germany.
“I had to walk to the sidelines to get my towel, something called 30°C sweat running down your hands. I needed to wipe my hands and he gave me a warning.”
Despite the sharp exchange, Kyrgios regained his composure to win the next two sets, sealing a 5-7, 6-2, 6-4 victory over his Greek opponent.
He delighted the crowd with some amazing shots during the competition, a reminder of what makes him a dangerous player on the lawn.
“The support I’m getting from fans all over the world is amazing. They want me to go out and put on a show,” he added.
“I’m glad I’m still able to produce this level through the tournaments I’m playing. It’s a testament to how hard I work when I’m not playing.”
Kyrgios, whose outbursts on the court often make him a divisive figure among tennis fans, is not seeded in the tournament but now faces Spaniard Pablo Carreno Busta in the next round on Thursday.